I had a full medical exam last year, I need to lose a lot so was very uncomfortable.
I was given a gown to wear and I did have to have a breast exam so was topless, but it was very discreet and I only had to open the gown not be completely topless.
Not sure why you would need to be naked or even topless for a full exam, I had blood tests, eye tests, ears checked well basically everything.
If you are not comfortable make sure they give you a gown, tbh I think they will but if not ask.
You will be fine i'm sure, they have probably seen a lot worse things than you
Good luck and try not to worry, I know its hard, I did worry, but honestly there was no need to.