Once cooked, the protein is severely denatured. Some people can handle it once cooked. My child when younger was so severely allergic that my wife would eat something with egg in it (not even the egg, just something with egg as an ingredient, like a cookie or bread) and even once denatured through cooking and absorbed by her body, he would still develop bleeding skin reactions within an hour of nursing. She was on a total elimination diet for years. Af four years old (yes, he still nurses) he can handle eggs through breastmilk and can also handle foods cooked for a long period of time (like, he can eat cake but not cookies, cake have a lower egg concentration to begin with and are typically baked 40 minutes or more, veruss 15 for a cookie).
Long-winded way to tell you to determine the severity of his allergy. When my son was first skin tested, his egg reaction was larger than his pure histamine reaction. There is no surefire way to determine how severe the allergy is, but many AI docs can give you an educated guess.
The pizza is safe, the chicken nuggets never are, macaroni was once. The buns are fine, PBJ is fine. Most CS locations will make him grilled chicken in lieu of nuggets upon request. There is a complete ingredient list available for almost all items.