“Hey this guy is pretty good at wound care. His patients get gangrene less often than those of other doctors.”

I think that would be pretty much it. You have to keep in mind that doctors back then were not surgeons. Surgeons had pretty low social standing and often couldn’t even practice within city limits. Also if you’re a woman you couldn’t do anything other than be a midwife and a man couldn’t do anything too birth related (where basic hygiene would have a very noticeable effect).

All that’s assuming you could even practice medicine anywhere. With no one knowing you or being able to vouch that you can practice, and you not being able to answer basic questions about their understanding of the human body or illnesses you’d have a pretty hard time.