Those are difficult allergens to avoid. Has your son shown reactions to those ingredients? Testing has a high rate of false positives, so a food allergy diagnosis shouldn't be based on test results alone.
We have milk and egg sections of this forum that you may find useful as well as a few corn threads in the other allergens section. I'll warn you, corn is the hardest to avoid because it's not a top 8 allergen and doesn't have to be labeled. Also, it's in EVERYTHING. To avoid corn, you're looking at primarily single ingredient foods - meat (but not if it has added broth/water/solution like most poultry), fresh fruits and veggies, dried rice and beans, etc. Many spices and even table salt contain corn. Often things like pizza crust, bread, etc. are dusted with corn meal. Canned goods manufacturers will dust the inside of the cans with corn starch before adding the food product. Toothpaste contains corn. Most medications contain corn. Chances are your son is unknowingly eating/exposed to corn a lot. The good news is, if he's not reacting, he's probably not allergic or at least has a very high tolerance and can just avoid obvious corn.