And yes many kids outgrow food allergies
My oldest daughter, now 4, experienced the same thing the first time I gave her yogurt. She didn't like it so I didn't give it to her again. When she started drinking milk at one year old she would get a red face where the milk touched. Her poop was frothy, that is the best way I can describe it. My husband was in med school at the time and I (stupidly) assumed it was normal if he didn't mention it being weird. I just ignored my intuition. At 10 months she grabbed a piece of scrambled egg off my plate and before I could react she had stuffed it in her mouth. She immediately broke out in hives and fortunately she was okay with a dose of benadryl (visited dr immediately).
At her one year visit the ped recommended sending her to an allergist to check for egg allergy because of the slight chance of allergic reaction to MMR vax. She tested positive to egg and strongly positive to milk.
Based on my experience I would immediately halt any milk in her diet. Not sure about yours, you would have to ask her allergist. I never watched what I ate other than avoiding peanuts and a few other tree nuts (spouse is allergic).
My oldest never came in contact with egg again until she tested no longer allergic at 3 1/2. She outgrew milk at 2 1/2. She can now eat anything. We did wait to introduce peanuts and tree nuts, fish and shellfish until she outgrew the egg allergy.
With my 4 month old she will not touch a drop of milk or egg until after her first birthday and still not sure about when I'll feel comfortable. You have to be so careful, they hide that stuff in things you wouldn't even think.