Mother Mother I Feel Sick Send for the Doctor Quick Quick Quick by Remy Charlip and Burton Supree, illustrated by Remy Charlip

From chapters.ca:
Cherished household items are mysteriously disappearing. And a rotund little boy feels ill. What's a mother to do? Why, call the doctor, quick, quick, quick! After one look at the boy, the doctor decides to operate and investigate. But no one is quite prepared for what he finds. Acclaimed children's author and illustrator, Remy Charlip, presents an updated and expanded version of his original, fanciful story.‚ Great source of inspiration for classroom and at-home shadow play‚.

Froggy Goes to the Doctor by Jonathan London, illustrated by Frank Remkiewicz

From chapters.ca:
Froggy is going to the doctor for a checkup, and he's feeling a little nervous. "What if the doctor wants to give me a shot" he thinks. He worries as he dresses and then he can't sit still in the waiting room. Finally, it's time to go in and change for his exam, but ... OOOPS! He's forgotten his underwear! And that's just the beginning of Froggy's hilarious doctor visit that ends reassuringly with a gold star and a lollipop.

Ernest and Rebecca vol 1: My Best Friend is a Germ by Guillaume Bianco and Antonello

From chapters.ca:
Rebecca is a six and a half year- old girl who is out of luck - her parents are on the verge of divorce and she is always getting sick due to a weak immune system. One rainy day Rebecca's luck changes when she meets a magical microbe named Ernest, who becomes her best friend! Ernest is no regular germ - he's about the same height as Rebecca and he can talk. Can Rebecca keep her parents together with the help of her new friend? And can anyone really have a friend who belongs in a Petri dish?

Iris has a Virus by Arlene Alda, illustrated by Lisa Desimini

From chapters.ca:
Iris finds out that having a stomach virus is exhausting, especially when her brother, Doug, lets her know that she always gets sick at the wrong time. The sibling rivalry and misunderstanding of what germs are when they are called bugs unfold in this light hearted story of Iris's ordinary illness and her unfounded concerns. Arlene Alda's engaging prose, interspersed with rhyming couplets and complemented by the quirky, vibrant cut- paper collage illustrations of artist Lisa Desimini, make this book a must- have for any child who has ever had more than a runny nose.

The Fault in Our Stars by John Green

From chapters.ca:
Despite the tumour-shrinking medical miracle that has bought her a few years, Hazel has never been anything but terminal, her final chapter inscribed upon diagnosis. But when a gorgeous plot twist named Augustus Waters suddenly appears at Cancer Kid Support Group, Hazel's story is about to be completely rewritten.

John Green is also part of the Vlog Brothers project and Crash Course.  I highly recommend both his books and his internet projects.

A Sick Day for Amos McGee by Philip C Stead, illustrated by erin E Stead *rec

From chapters.ca:
Friends come in all sorts of shapes and sizes. In Amos McGee's case, all sorts of species, too! Every day he spends a little bit of time with each of his friends at the zoo, running races with the tortoise, keeping the shy penguin company, and even reading bedtime stories to the owl. But when Amos is too sick to make it to the zoo, his animal friends decide it's time they returned the favor.

People Who Help Us: Doctor by Amanda Askew and Andrew Crowson

From chapters.ca:
With bright, lively illustrations and easy- to- read text, People Who Help Us introduces young children to the different jobs that help people in the community. Useful notes for parents and teachers give a guide to reinforcing childrens understanding of the text and explain difficult concepts through interactive reading and activities.

The Sniffles for Bear by Bonny Becker, illustrated by Kady MacDonald Denton

From chapters.ca:
Bear has a terrible cold. In fact, Bear is quite sure that no one has ever been as sick as he is. So when Mouse comes tap, tap, tapping on his front door eager to make Bear "as good as new" by reading a sunny story, singing a rousing chorus and plinking a twangy tune on her banjo, the pitifully coughing Bear - growing weaker by the minute - is convinced that his tiny friend does not appreciate the gravity of the situation. Can there be any saving Bear from his certain demise? Welcome the world's most lovable curmudgeon and his endearing, unstoppable sidekick in a wry new comedy sure to have even red- eyed, sniffly- nosed readers rolling with laughter.

Sneezy Louise by Irene Breznak, illustrated by Janet Pedersen

From chapters.ca:
Even before breakfast, Louise knows that it isn't going to be an easy day. Her itchy eyes, wheezy throat, and very, very sneezy nose lead to trouble at school, during ballet class, and even while reading a bedtime story. Irene Breznak's rhythmic refrain is "catching" as characters implore Louise to "cover your mouth, PLEASE!" a message that parents will appreciate! Janet Pederson's charming watercolors bring Louise to life as well as that tickly, sneezy feeling familiar to everyone!

The Flea's Sneeze by Lynn Downey

Everyone in the barn is sleeping and no one hears the flea's desperate pleas for a tissue. They won't be sleeping soundly anymore when he lets out a gigantic sneeze.

Miss Polly Has a Dolly by Pamela Duncan Edwards, illustrated by Elicia Castaldi

From chapters.ca:
Children have been chanting "Miss Polly Had a Dolly" for centuries. But the original rhyme only had eight lines. Now for the first time, Pamela Duncan Edwards expands on the original to answer the question of what happens next (they all go out for ice cream when Dolly is feeling better). Newcomer Elicia Castaldi gives Miss Polly an amazing new look that perfectly matches the spunky rhythm of the text. Musical arrangement (for piano and guitar) with finger play instructions are included on the endpapers, so kids can sing along and act out the words.

I'm Getting a Checkup by Marilyn Singer, illustrated by David Milgrim

Everyone needs to get a checkup at the doctor sometimes and, if you don't know what to expect, it can be scary. This book details most of what happens in a checkup in excellent and simple detail.

Riley Socks by Leahnne Allen, illustrated by Gary McDaniels

An inspiring picture book about one little girl's fight against cancer, Riley Socks is an excellent book to introduce the topic to children or a good read for anyone embarking upon the same journey.

The Little Elephant With The Big Earache by Charlotte Cowan, MD, illustrated by Elaine Garvin

From chapters.ca:
After a busy afternoon of making mud castles with his cousins, little Eddie awakens at night with a terrible earache. His mother takes excellent care of him and Dr. Hippo reassures them both the next day. Will Eddie recover in time for his birthday party?

The Moose With Loose Poops by Charlotte Cowan, MD, illustrated by Penelope Neal

From chapters.ca:
Four year old Miles develops a tummy ache while on a family picnic in Maine. His planned camping trip with Papa (complete with canoeing and fishing) is postponed when throwing up (oops!) and diarrhea (loose poops) develop. Mama, Papa and Lucy Moose take excellent care of Miles at home helped by their kindly pediatrician, Dr. Hippo. Of course, Miles recovers in time to camp with Papa under a special, star filled sky.

Sadie's Sore Throat by Charlotte Cowan, MD, illustrated by katy Bratun

From chapters.ca:
In her story, Dr. Cowan empathizes with small children who are often confused about being sick and scared of going to the doctor. She writes with gentle humour and encouragement, showing children that there is nothing to be afraid of. Her story is as educational as it is entertaining and will provide comfort to both parent and child.

Peeper has a Fever by Charlotte Cowan, illustrated by Susan Banta

From chapters.ca:
In her story for children ages 4-8, Dr. Cowan empathizes with the aches and chills and misery of small children with fevers. In Peeper Has a Fever Dr. Cowan captures the unhappiness of her patients and writes with confidence and humour to comfort them. Peeper's story is as educational as it is entertaining and will offer reassurance to any parent and child dealing with fever.

Katie Caught a Cold by Charlotte Cowan, illustrated by Katy Bratun

From chapters.ca:
In her story for children ages 4-8, Dr. Cowan empathizes with children who are feeling miserable with a cold. She understands about their stuffiness and sneezing, feeling tired and thirsty. In Katie Caught a Cold Dr. Cowan illustrates the comforting care that can help children feel better and thus reassures both parent and child.

Chicken Pox! by Shen Roddie, illustrated by Frances Cony

Chick has the chicken pox and they itch like crazy! He tries everything to make it stop. What will work?

Felix Feels Better by Rosemary Wells

From chapters.ca:From chapters.ca:
Felix ate too many chocolate blimpies, and he doesn’t feel well. Not even Mama’s dose of sugared prunes helps him feel "perkier". So off to Doctor Duck he must go. "Don’t be afraid, my little moonbeam", says Mama. But Felix is afraid. Best- selling author and illustrator Rosemary Wells applies her rare ability to tell a funny, heartfelt story about a common childhood experience: going to the doctor.