How about a predator prey model? It was one of the first things I studied related to modelling in one of my differential equations courses, and could be relatively simple, but still interesting if you choose something cool?

Or, since you're a health care professional, would you be interested in a tumor growth model? I haven't looked into this deeply myself but I believe there are both ordinary and partial differential equation models, and you could choose one that is relatively more appropriate according to what you've done in your course.

(Also would have suggested a simple SIR model but seeing as you've worked on likely similar stuff, I'll leave that aside for now, unless you want to do that as well/instead)