My knowledge is aged but probably still partly true.
Aerospace Medicine is the body of practice centered around the health and operability and safety of humans in the flight environment. That makes it a catchall, but they turn their noses up at us groundlings.
Despite what they tell you at the recruiters, actually little of what you do in the mil transfers over to civilian credits. It does give you a grounding in the subjects, and that is what appears well in your resume. If any schools are offered, you take them and excel. If they offer to send you to or pay for a civilian school, jump on it. STart corresponding with civilian employers (and schools) early to see who values the mil experience and what they really want in the way of classes/prereqs, than start taking them off-duty.
The majority of what they (used to ) do is run clinics, give shots, and do flight physicals for aviators and other air crew members. A small selection of them used to actually do aeromedical transport. A smaller bunch did barometric medicine (pressure chambers).