My twin sister suffered from complete adrenal failure one year ago, and then after being classified as an Addisonian, her adrenals started working again. So her case would be pretty classic adrenal exhaustion... she never had any symptoms like this with breathing. You might want to check food allergies, and maybe check for the presence of mold in the house. Are you absolutely positive that environmental issues are not to blame? Has he been tested for the typical usual allergies? Just curious about that.
My sister's symptoms were mostly severe fatigue. In addition, she had a shaky feeling at times that was not related to sugar levels (she would test when this happened and glucose would be normal) -- she thinks that this was her body struggling to produce adrenalin/cortisol. She had some digestive tract problems, too, and this is a typical symptom. But no problems with breathing. If I were you, I would ask to be referred to an allergy specialist if he has not already seen one. Some food allergies can cause this kind of reaction, so don't stop with environmental checks.
One thing to check is whether his breathing tract (nose, etc.) is constricted. I have a collapsed nasal valve -- one side of nose around the opening to the sinus has lost the support tissue and tends to just fall in on top of the sinus opening and thus blocks it. I suffered extensively for several years and was using prescription nasal sprays constantly. I had a turbinectomy (nose surgery shaving the inside engorged tissue to widen the passage in nose). Afterward, the inside of the nose got sticky during the healing process and I started waking up in a panic feeling I was strangling and then I suddenly developed high blood pressure and tachycardia (rapid heart beat). I had to go to a special sleep disorder clinic and found out that many people have problems with blockages affecting the passage of air from the nose into the lungs. It is worth a quick check -- breathe on a mirror, visual check of size of both nostrils -- I would try using Breathe Right strips for a little while to see if the widening and added oxygen cures it. If so, you've got your answer. If not, a trip to the doctor might be in order.