Whether it's for an emergency or just a checkup, going to the doctor is never fun for a kid. They're possibly nervous about what the doctor will say or what they will do. Then they notice a poster on the wall of one of their favorite athletes and a lighthearted story about a time that they had to go to the doctor for a similar reason. For example, perhaps a kid that's sitting in the ER because of a broken arm notices a large poster of Alex Rodriguez with a short story about how going to the doctor made their broken bone all better. Suddenly, the kid feels less afraid, knowing what good company he or she is in.
This idea would be implemented quite easily, even in its most elaborate form. If celebrities are willing, which most of them probably would be, it would be a simple photoshoot and short interview about the injury they had as a kid. While the images could be pretty standard, it would be far more fun to look at if the celebrities were acting out the scenario or, if what they're talking about is a bit more serious, perhaps they could simply appear supportive and positive. The actual photoshoots could be outsourced to reputable photographers. While the images are primarily meant to be exclusive the hospital, they could also double as promotional material in whatever way the hospital sees fit.