My 5 year old is allergic, and I mean anaphylactic to eggs, milk, peanuts, also allergic to cats, dogs, several trees and grasses, etc, so I completely understand your frustrations. Ask your allergist for a sheet with ingredients you need to be aware of (hidden milk derivatives like sodium caseinates, whey, caramel color.) It's usually pretty thorough. As for foods your toddler can eat, potatoes have been our friend! (No french fries from Mcdonalds, they have milk derivatives in them and he may not visibly react, but his airways will!)
Lots of chicken, veggies, meat variations and fruit are going to be your new best friends. In case he has a birthday during this, there are cakes without those ingredients made by CherryBrook Kitchen. Kroger sells them. And as for a good cheat snack? Regular OREOS! You are now an official label reader, my friend. Hopefully he'll outgrow them soon.