I Had What I Thought Was A Chest Cold 10

I had what I thought was a chest cold 10 weeks ago. All other symptoms have subsided but I still have a horrible cough that's preceded with wheezing. I've never had chronic cough and as far as I know do not suffer from asthma but I know when I'm going to have coughing because first comes the wheezing then I will cough, wheeze, cough until eventually I will vomit what appears to be nothing but mucus. And after coughing I always have a metallic taste in my mouth with is quite irritating. I am not on any current medications. I do not suffer from any ulcers and have very good oral health. Any suggestion as to why the cough and wheezing is holding on?