It sounds to me like a case of dry skin. Keep applying a moisturizer.
Also: your parents do NOT have to be in the room when you get examined by a doctor. Secondly, if you tell your doctor you masturbate, he won't tell your parents. Thirdly, just tell your parents you have this problem and you want to see a doctor about it. You're old enough to know when something's not right with your body... old enough, in fact, to have enough privacy from your parents. If you still feel uncomfortable, talk to your dad about it... it'll probably be easier!