A lot of kids with an egg allergy are ok if it is in something like muffins since one egg spread across 24 muffins is an almost insignificant amount per muffin and doesn't directly touch the child's mouth/throat etc.

Some also do ok with part of the egg. My oldest - 28 years old now daughter doesn't do well on a regular egg but is ok with the liquid egg you buy in the dairy section. If an egg is scrambled she does better - ie the yolk and white are mixed together. Her reaction was always just a milk stomach ache and she ate eggs growing up just not before a major event.