I have had a lot of experience with allergies, myself, my children and my own siblings. The best thing to do to elliminate food allergies is to stop giving it to him for 3 days then try him on it again and see if he reacts.
Or even stop for a week if you can and see if his excema clears up. It is hard not to eat dairy or gluten for a week when you are used to having it as part of your every day diet but it is a good way of telling if there are food allergies there.
My brother and sister used to get coughs, wheezy and excema from dairy products, and as my doctor put it 'cows milk is made for baby calves, not humans' lol
Good luck!