I Have Had This Really Bad Cough For 2 Weeks.

I have had this really bad cough for 2 weeks. Initially it started out like a cold and I took some over the counter flu tablets but then it turned in to this really dry cough where I cough then choke, gag or vomit. I haven't slept properly since I got this as I haven't been able to avoid the coughing fits in my sleep. What do I have? Is it a chest infection?