DS2 ended up tiny - I mean tiny as far as being a man is concerned. (5ft4)
We were told to 'go away, he'll have a late growth spurt' and then told 'you've left it too late, his bones have fused - he can't take growth hormones now.' With hindsight I would have pestered for more regular check ups but DS had a host of other medical problems and I was really concerned he was getting conscious of being 'not right' and 'not normal'. But if your DS's health is otherwise fine, i would push very hard to keep referrals regular and to explore all options.
Society is cruel to short men - no two ways about it. Loads of women refuse to date a short man and - my particular hate - think that any man who happens to be short and a not wholly charming has 'short man syndrome' (My take on this is that a huge number of other men must have 'everage height man syndrome' or 'tall man syndrome' to account for their aggression or drive or neuroses.)
DS went through a phase of being extremely down about it. Of believing he'd never get a girlfriend. I did a load of confidence work with him. I made a Pinterest of gorgeous, successful short men who got the girls and plain, ordinary short men who were happily married and successful in their jobs. We found fashion blogs by short men and articles by women who said how much they adored their partners who were several inches shorter than them.
DS met a lovely girl and they dated for several months. They split, but that made him realise that it's possible to find love. He's recently started dating online again and hasn't found height a barrier at all so far. He still gets checked at the door of lots of clubs and bars, and recently went on holiday to Scandinavia where men are both tall and blunt and was told with astonishment, 'Man you are short like a child!' by hotel porters etc but these days he just doesn't care. He's even done some modelling for a menswear brand.
My advice is to encourage him to decide not to feel resentful about it. and not to compare himself to other men. Keep saying - the world needs all sorts of people in it. It thrives on diversity. He can't change his height but he can choose how he copes with the social prejudice about it. Short men with a positive self-esteem do far better in job interviews and in love and socially than ones who feel bitter and depressed about it. DS has been both and he now sees that his attitude is everything.