This is, indeed, a challenging question. It is possible that there are other agents in the diet soda that, in some way, potentiate the effects of the diet substitute that causes these hives. For now, unless you are willing to see a board certified allergist and have tests of all of the ingredients of these drinks, I would suggest staying away from diet sodas for a while and make sure the hives are gone. If this is the case, you might look at trying different drinks that have different products in them to see if the hives come back.
Eggs can be an allergic food,and also sweetners can be ,Google it and get a list of foods to be careful with.