My ds used to break out with eczema when he was a baby. I also noticed that whenever he had grated parmesan cheese he would get red all around his mouth and face. I stopped giving him dairy and the eczema cleared up. I never had him tested though and now that he's 8, he eats dairy all the time with no problems.
Same with our DS17. Every winter he would get bad patches on his face. He stopped drinking milk and hasn't had any since. He can drink some milk, he usually has some chocolate milk with his school lunch and will have cheese with some foods, etc. but he no longer drinks regular milk. I don't know that it really is an allergic reaction vs just a reaction to milk.