Shortness of breath with cough

I normally get a cough with a cold and my Dr says it is from my sinuses and he would give me antibiotics to clear it up which it did.  This year the Dr refused to give me an antibiotic as he said I wasnt coughing up green phlem but I can never get up any phlem as my cough it just a hard cough.  Well, it got worse and after 5 cough bottles the cough is now much looser but my breathing is very bad and I have a wheeze in my chest.  When I lye down the noise in my chest is like a cat bawling, a sort of rattle which sounds like bronchitis but my Dr now says I may have Asthma and has given me two inhalers,  a reliever and a preventer.  He also sent me for a chest xray but I havent had results yet.  I have been using the inhalers for past 3 days with no improvement.  I did get some phlem up today for first time and its green.  I feel I have a chest infection.  Has anyone an opinion on this, please.