Allergies?

My son was sick for awhile, got steroids got better. Well we went outside and my brother’s in-laws dog touched my son’s face when he sniffed him, now my son is stuffy, sneezing and has a wheezing like breathing again like he was when he was sick. Well I just realized that when my son was sick the last time, it was after my brother in law took his dogs upstairs(where we live, he lives in our basement but doesn’t normally come up) for the week he was sick, to give his dog a bath, and every time he showered his dog come up with him because the dog was getting into things and tearing them up. Anyways my son got better the 3 days the dog wasn’t around and now that the dog come back, he’s sick and has a rash. Could this be allergic reaction to the dog? I don’t know if babies can have these problems