Breastfeeding and egg allergy

Moms that breastfeed or breastfed in the past:

I have an 8 month old and I just let him try eggs for the first time. He got a mild hives rash! To be sure, I am going to get him tested for the allergy at the doctor. My question is, how does this affect my diet and breastfeeding? When I look it up, it says that intact allergens can pass through breastmilk! But eggs are in so many things that I eat all the time and my baby is always happy... I haven’t noticed any reactions or digestive upset with him at all. My reading makes me think that I would need to avoid eggs also... does anyone have experience with this?

Note: I am very careful with food introduction. The day that it happened, that was the only new introduction. I did take him to the pool but it was his 5th pool trip. No other new foods or products that day! I’m also looking into the chlorine/saltwater status of the pools that he has been to.