I think people can be allergic to everything... Unfortunately.
Hello,
I have that exact same problem. I love eggs too, but, they don't love me. However, a food allergy test DID reveal allergies to eggs. UGH.
I have found that if I buy "organic" eggs, I don't have this issue, it seems that whatever they feed the chickens in the culprit for my tummy pain, but, the "organic" ones don't seem to have that "ingredient" in them. Give it a try, it might help.
Oh, and I, too, can eat them when they are in other foods, maybe because I am not eating as much of the egg that way.