First thing is to get him checked by getting a referral from your family practice physician to a pulmonary specialist. Now, it may turn out to be something like a sensitivity to dry air. There's a reason people on oxygen therapy, even for short periods, are routinely given the benefit of a humidifier in the oxygen line. Cold, dry air or dry air alone increases airway resistance. Obviously, few divers have a repeated severe reaction to dry air or we'd all be complaining.
But you may also find that it's an early stage of another condition. A number come to mind, and it's pointless to speculate. That's what the specialist is for. Some of these conditions are progressive, and starting treatment early can help a great deal and can certainly make life more pleasant. What I would not do is let it go until he eventually quits diving and gets some relief but looks no farther into it.
You now have the classically difficult task of getting a man to go to the doctor. Good luck on that if you've got one of the difficult variety.
And the way he breathes may or may not have something to do with how he suffers afterward. If dry air is a problem for him, more rapid breathing of that dry air will make it worse. He may be simply not so god a breather as you (it's a skill), or he may be larger and therefore use more air, all other things being equal. But it may also be the other way around, that his respiratory rate is elevated on account of some condition. If his lung workup turns out with nothing abnormal, then he can maybe work on breath control, confident that it's not pathological. If it turns out he's just over sensitive to cold, dry air, after all other possibilities are explored, it might even be something that could be helped with medication, maybe a cholinergic antagonist or something. I don't know if that's done, but the specialist can tell you.
