I would agree with most of what has already been said. Unfortunately, everyone is different and different things will set off people, eg cats, dogs, etc. I agree with those who have sadi you will need to learn as you go along what affects your son and how to handle it. However, my daughter has gone strictly non-dairy and it has helped eczema, as well as ashtma. Re the asthma, she also has rhinitis. The non-dairy helps the rhinitis, which in turn helps the asthma because she can breathe properly through her nose.
She has also benefitted from a very good asthma nurse. You definitely need someone who has this expertise and understands it. Our new asthma nurse is better than our old doctor because it is her specialist area. Also she has prescribed my daughter a new type of inhaler, a two in one which acts like the brown inhaler (long term) and the blue (short term) all in the one. This has proved very effective and has definitely improved. She now only takes the inhaler occasionally whereas at one time she was using the blue inhaler several times a day. The nurse said this meant that the asthma was out of control. Previous people have said this but medication has improved in leaps and bounds and your sone should be able to lead a normal life with medication as and when he needs it. Keep pressing the doctor/nurse if you don't feel he's getting everything necessary.
Best of luck, I do understand how difficult and frustrating it can be. Just as a by the way, my daughter has ended up in hospital twice, as a result of reaction to aspirin. Apparently (we now know) this ia a common substance which can affect asthmatics - watch our for it in cold reliefs.
Tina