Yes some people can suddenly become intolerant to eggs and then have stomach aches, bloating, vomiting diarrhea etc.
My sister used to be able to eat eggs and now that she's 40 years old she has an intolerance to eggs and can no longer eat eggs without getting sick from them.
She loves eggs and wishes she could eat them and although it's not life threatening to be intolerant to eggs it's still not a good feeling when you eat eggs when you've become intolerant to them.
Some people are born intolerant to eggs while other people like my sister become intolerant to eggs later on in life.
If you do experience bloating, stomach aches, diarrhea etc after eating eggs and you're intolerant to them then the feelings and symptoms will go away within a day or so.