I’ve never experienced this with either kid but I’d go to the ER. Preferably children’s hospital if it’s close
It's extremely rare for babies to have anaphylaxis; even if they are allergic to something, the reaction isn't likely to be detrimental. I have random allergies, so before starting solids with my baby, I bought some children's allergy medicine (you can get liquid benadryl or zyrtec) and the few times we have needed it, we called the 24 HR nurse line for info on accurate dosage and what to do. If your baby is wheezing, goes blue in the lips, has tongue swelling, or has hives on their neck or chest, then administer the allergy meds (if you have them) and head to the ER. If it's a severe reaction and you do not have allergy meds, 911 would be better so that they can treat ASAP. We have taken our kiddo to urgent care after allergy meds because she was splotchy on her chest as well, and it was a new symptom for her reactions. (Repeat exposures can cause worse reactions.)
I've known parents who feed common allergens (egg, dairy, soy, peanut, fish, etc) in the parking lot of a children's hospital emergency room. I think that's smart! Or....you could ask your pediatrician for an epinephrine pen prescription and pick it up at your pharmacy. Be sure to ask your pediatrician to demonstrate how to use it or the pharmacist helping you at the pharmacy. You need to be confident you can use it in the event of a reaction & need to act quickly. Hope it helps!!