A surgeon whom Parry considered a mentor had cut out heart and shark shapes to decorate children’s bandages, and Parry, who had always enjoyed doodling and drawing, decided to follow suit, he said.

One of the most traumatic days of Susan McFrederick’s life was watching her son, Witt, being wheeled away for surgery to fix a ruptured intestine hours after he was born in 2011. But after the ...