I'd say any kind of crowded public transportation is probably just as bad as a hospital in terms of germs and the like.
Nothing compares to hospitals, never touch anything in a hospital there the most disease ridden place you can imagine, washing your hands in most places won't really matter, but in hospitals there are so many diseases it's not fit.
Most of those germs you should be afraid of like fleshing eatings virsus or viruses that destroy the heart are all traffic 90 percent of the time through hospitals
Even if they devote loads of money and time restricting germs and shit theres so much floating around in hospital that they can never keep rid of it.
Nurses get sick often, just like everyone else, however some places are very liberal with their sick time because of this.
Doctors I'd think get sick more often than most people, but get sick for shorter periods of time having less prevalent signs of it, and know better than to be sniffling in front of their patients.