Also my main concerns were that which type of doctor can I assist to convince my parents about this procedure? And about the girl thing, tall women do date short men its all on the man hitting right on the spot but height doesnt make a difference... unless it is a whole feet which is what I am trying to Avoid. Being 5'6-7" could bring me some advantage alreay
First off, you probably won't even have the money until you are 18, anyways (unless your parents want to pay for it). As for the doctors, that can be tricky. Most doctors aren't going to recommend leg lengthening for cosmetic reasons. You could reference them to Dr. Paley, Dr. Guichet, Dr. Betz, etc. if you were to do a consultation with them.
If I were you, I'd probably do about six inches (15 cm) of lengthening altogether--say, about 3 inches on tibias and 3 inches on femurs. If you do that and bulk up some, you'll have a tremendous increase in social respect and status. If your proportions warrant it, you are very fit, and you are willing to put up with some time and pain, you might be able to do 8 inches altogether, but that would only be if your doctor gives you the go ahead. Some people can do 4 inches per segment, but it certainly isn't for the faint of heart.