This is a forum for Attention Deficit Hyperactivity Disorder (ADHD). I think you might want to try another forum. However, I do know that growth hormone is given to children who have a severe growth problem. Whether your son's growth problem is severe enough, I don't know. I am also not sure at what age the treatments are started.
I assume that since you gave his measurements in centimeters you are European. Reason why is that I was going to suggest soccer (or football to you guys) as a sport where height is not as important - witness many of the Spanish players in the recent world cup finals. Tennis is also a good sport. In fact, Diego Forlán from Uruguay (winner of the Golden Ball) excelled in both.
Some people are short. That should not be a problem, unless you make it one. Tall people are not better people. I have a son-in-law who is 5'6". He is famous in his field, has fathered four children, and his height has never bothered him. My own father was even shorter and women found him devastating (unfortunately for my mother). Bigger is not better. But assuming it is, is a problem. I would not seek treatments to increase his height.