My 1 Year Old Has Had A Cold With Major

My 1 year old has had a cold with major runny nose for the past month. I thought he just got a cold passed to him from one of our other family members bc the other 4 of us has has one. We went in to get his shots and they wouldnt give him the live shot and said he needed breathing treatments. That was 2 weeks ago. He hasnt gotten any better or any worse. The only thing that he has changed in his life is starting whole milk. Could this be an allergy or something to milk?