So what goes on, do you have to change into a gown or something?

The chances of someone being able to answer this for a particular facility and for one appointment on this website isn't very good. Are you asking what the typical physical would involve for a 15 year old girl? Perhaps there's a physician who could answer that more generally. Otherwise, call this particular pediatrician's office and ask a nurse what you can expect - they will be more than happy to tell you. I'm sure they know that for young people, there'sd some apprehension and discomfort about upcoming appointments.

Is there a problem with changing into a gown ?

Yes you have to change in to a white papery gown. The doc will leave the room and then you change out of every thing except for your undergarments