It's hard to say! I have read they can grow out of it by the time they are 5/6 or they could always have issues with eggs. I'm not sure if it depends on the severity of the reaction either. My LO is "mildly" allergic to eggs, he got red weals the first time he had just egg and his face went bright red with swollen eyes and ears after an eggy pudding. With hindsight egg in things makes his reflux worse so we avoid all egg. If it is an allergy then more exposure can make it worse, not sure if that is the case for an intolerance or not.
He is supposed to be having an egg challenge when he turns two to see if he still has it - should be interesting!
Laura