Men can control their sexual urges. Those who can not have a mental problem unrelated to the masturbation. You don't avoid compulsive hand washing by never washing your hands. The compulsive disorder is the symptom of a deeper disorder. It's the same with masturbation.
Compulsive masturbation is the symptom of a deeper disorder.
And frankly, punishing someone, trying to make them feel ashamed for something that is natural, something that everyone else in the house is allowed to do is probably the best way to cause a disorder. Secondly, I don't know what kinds of medical journals this person is reading, but I have never seen anything, anywhere, that says masturbation will stunt the growth of your penis. And unless this doctor can produce the scientific evidence that says otherwise, I would say this person is practicing bad medicine. You are going through puberty. People develop at different rates.