Could it have something to do with the sulphur in eggs as in Onions etc too?
and if so, why?
You seem to be suffering from allergy to egg proteins. Most people who are allergic to hen's eggs have antibodies which react to one of four proteins in the egg white. These proteins are named ovomucoid, ovalbumin, ovotransferrin, and lysozyme; ovomucoid, also called Gal d 1, is the most common target of immune system attack. The egg yolk contains several potential antigens: livetin, apovitillin, and vosvetin.
A person who reacts only to a protein in the egg yolk may be able to easily tolerate egg whites, and vice versa. Some people will be allergic to proteins in both the egg white and the egg yolk. Egg yolk allergies may be somewhat more common in adults. A small number of people who are allergic to eggs will develop an allergy to chicken or other poultry meats.
So I guess the best treatment is to avoid eggs.