Hi A.,
The good news is if you get in the right mindset and find physicians who will work to heal your children instead of treat them, you can reverse this over years. I am a fully experienced mom, aunt, godmother of children littered with allergies. Some now able to have regular diets, and some able to "cheat" now and again with little to no reaction.
Have no fear - there are so many things to feed him that do not have milk. The egg gets a little harder, but my friend uses tofu and egg replacer for the baking and limits store bought snacks to non-processed. CherryBrook Kitchens has great mixes that are usually egg free. Check out GFCF diet sources and many times you will see the eggs removed as well. 1/4 Silken Tofu with liquid replaces 1 egg . Check Whole Foods or kroger in the organic section for the high quality egg replacers.
Rice milk and almond milk are perfect replacers for milk. No biggie at all. For fat and extra minerals add 1 tblsp cod liver oil to 8 oz cup. You can start with half that much if he is eating veggies and fruit well. Trust me, the milk is a just a piece of cake. We are just so marketed about milk that we get stuck. Focus on giving him some rice milk, but he should begin aquiring his calories from fruit, veggies, and meat. If you can get organic veggies and meat with no hormones, they will taste better and he will enjoy them. Give him dips (ketchup, applesauce - anything) to dip his little veggies in. Flavor with vegetable broth when cooking or steam them. Don't try to cover them, make them tasty.
I would highly recommend you reading the Allergy part of "Healing the Childhood Epedimics" by Kenneth Bock. If you have not done an IGG on your kids, you may consider it. Healing requires getting rid of the foods that cause inflammation, not just the ones causing reactions. Also, treating the yeast and underlying triggers is also important. Vaccine reactions target digestive vulnerabilities. Delay your vaccines until you are able to read and make informed choices about your childs medical issues. You will be changing their future - so when it gets tough, remember, you are changing not just their lives as children, but taking them through 40,50,60 years of good health.
I have a fabulous physician I work with. If interested, drop me a line.
J.