Unfortunately, I think egg intolerance is a definite possibility. Others on this forum have posted identical experiences with eggs, so hopefully they'll come by and add their thoughts.
I wouldn't pursue stomach calming remedies, because then you're applying a band-aid rather than addressing the underlying cause. Listen to what your body is telling you! If you are egg intolerant, going egg-free for a while might allow you to recover, and then you could reintroduce eggs at some point.
If you don't want to eliminate them completely, try eating eggs only once a week or so, and see how that goes. If you still get stomach aches, ditch the eggs entirely, at least for a while.