I think what you are asking is, what do you say if you are the doctor meeting a patient for the first time? I usually hear things like this: "Hey, how are you feeling? What brings you in today?" If you say "what's wrong with you", this is very brash. I wouldn't say this at the doctor. In your second option, "I have a sore throat" is ok, but "what about you" doesn't make sense here.

Hi Amir, Breaking the ice at the doctor's isn't really something seen as socially acceptable in the West. Health is a a private matter so people probably won;t want to share their ailments! You definitely won't have met them and they are sick! I wouldn't advise trying to befriend people at the doctor's Thanks