Hi there,
I feel terrible for your son 
I was diagnosed with migraines at the same age and was given meds; probably a low dose of amitryptiline I think. I have subsequently by different GPs been diagnosed with cluster headaches, 'sport related' headaches, and a bunch of other stuff.
What I actually think is the problem after a lot of research is teeth grinding (bruxism) which I think is caused by my tongue tie, tongue thrust pattern, and possibly hypermobility.
Does he have a tongue tie of any description? You'll be hard pressed to find a GP who knows much about this but there are starting to be links shown and TT is a relatively simple thing to fix. I've ended up with jaw surgery to correct damage done by my teeth grinding and at the age of 30 I'm seriously thinking about having my TT snipped!
Other things which have helped in the past are rolling up a bath towel into a tight roll, and lying down on the floor with my neck over the roll and my head dipping back. It relieves a lot of tension.
I have also recently started trying muscle activation technique with my physio. There are spots on my jaw, under my ear, and on the side of my skull which, if pressed, immediately cause a migraine sensation for me. If you keep working on them they eventually relax and relieve tension which prevents the headaches.
Does any of that sound feasible or worth looking into for your son?