My aunt's mother always dresses up for doctor's appts. It's like a social event for her, she will wear fresh stockings, blow out her hair, do her makeup, wear nice clothes. She goes and chats with all the other little old ladies, catches up with the receptionists. She goes to at least 2 appointments a week, but she's a perfectly healthy 80 year old, she's probably in better health than I am. So for her, its' her social event, instead of a temple group, she goes to doctors.
As for me, I don't really dress up, but it depends where I'm going and where I'm coming from. When I go to my derm, I dress up because he's in a really swanky office, and I feel out of place if I don't dress up. He's great though, I never have to wait, he's very thorough, and a really nice guy. Other times, I'm usually coming from school, so I would just wear what I wore that day, whether it be scrubs, jeans, or dressy clothes (depends on what day it was). If I'm sick, I really don't care what I'm wearing. I do always make sure to shave my legs and armpits before an appointment though, even if I'm sick. I don't want people seeing my hairy legs.