I had an injury in my upper back. The got similar advice from a doctor and the pain still lingered, the same as with you.
I am also 15.
I went to a physio. HE CLICKED MY RIBS BACK INTO PLACE! He also told me that taking time off is not gonna to put ribs back in (oviously). After doing this I went back to benching the next day and low and behold very, very little, if any pain. (Although my sets were only about 100pounds, still a big achievement when the bar used to cause problems.)
If you just went to a G.P. chances are that they don't know jack-all about squats, how to do the form correctly or injuries which can be caused by these kinds of activity.
Also squating at 235pounds seems to be pretty heavy for a 15 yo. As said before, is your form suffering because of a weight that is to heavy for you?
I suggest looking up the exact way to do squats, hell there's probably a 100 page e-book somewhere on them

.
But do yourself a favor and go see a physio. They will most likely know much more about squats than a doctor would.