Let's put it this way. I was about your size and height. When I was 15 and 16, I was throwing 72-78 mph. At 18 (my senior year in high school, I'd touch 87-88 mph). Four years later in professional ball, at 22, I was consistently 94-95 mph.
Will a good pitcher-specific throwing and conditioning program help you gain velocity? You bet! It did for me.