Egg allergy

My baby had an allergic reaction to eggs recently (his first time having them) and we saw an allergist who did a skin test. The skin test was positive for egg allergy and a few other things and we are waiting for the confirmatory blood tests. I’ve eaten eggs my whole pregnancy and since I’ve been EBF him and he’s been fine. I’m just wondering if I should avoid eggs to avoid further sensitizing him? Pedi and allergist didn’t say anything about this and I’ve done some research but can’t find anything definitive.