Coughing after eating

This started three-four weeks ago when I got a cold. Now I can't eat and sometimes can't drink without coughing terribly. I cough until I feel like I'm about to puke. Anyone have any idea? I thought it was maybe dairy or something, but it's with everything and it started suddenly. I even cough after drinking water. I don't feel sick, but when I'm coughing my chest gets tight.