What Causes Dry Cough And Difficulty In Breathing?

Still experiencing some very annoying lingering symptoms. Started with severe productive cough, presumably caused by major sinus drip. Had short course of antibiotic (doc said the virus often was followed by bacterial infection). Now cough is dry, only a handful of times each day, but is accompanied with gag reflex (feel about to vomit, but never do) and intense salivation. At its worst, breathing was impeded by a plug of mucus in airway--had to gasp for breath before being able to cough it loose. Even now, there is sometimes a gasping for breath, frustrating since when I do succeed in coughing, nothing comes up but eventually I can breathe. Is this a normal progression? Will it go away on its own sometime soon? Thanks.