Could my 5 month old be getting sick from something inside our house?

My son has been having respitory problems since 2 months old. He got RSV at 2 months, wheezing, coughing and the like. at 3 months, we took him back in and found he had bronchitis - the following day it turned into pneumonia. He was in the hospital for 3 days, and released with antibiotics for the bronchitis. Just last week we had to take him back in for shallow rapid breathing, and the cough and congestion are back. Now they are saying he has Reactive Airway Desease , put him on breathing treatments every 4 hours, and steroids for the next 5 days. He is still coughing and wheezing, i feel terrible and cant figure out what is causing it. I know our duplex has had the same carpet for a long time, was not changed when we moved in, or the previous tenant. we have 2 cats that are indoor / outdoor. wondering if it is environmental.... :( any help would be awesome!