Milk and peanut allergy

My 9mo has dairy one day (like 1/4 cup a yogurt) and got red bumps all over his face. We gave him Benadryl and he was fine after 20 minutes (his breathing was not impacted). So we waited a few days and gave him a little peanut butter (like 1/8 tsp) and same thing happened. We have an appointment with his doctor for his 9mo check up and so I’ll be asking a lot of questions there but I just want some insight now please. Talk to me about allergies vs. sensitivities. Can he grow out of this? Etc... anything really. Thank you!!!