I've never heard anyone saying "la médica" not even in a hospital. Even when the degree female receive says "médica cirujana", in Mexico everybody say "la doctora".
For other professions:
La ingeniera
La arquitecta
La abogada...
Although "doctora" also could mean a female with a PhD. For instance, you could say "la doctora en psicología". That means she has a PhD in psychology.