It's possible that the Gastroenterologist was not able to see an erosion in your mucosal lining when he performed an endoscopy. I would consider talking to your doctor about a pH study ... these would determine if you are refluxing or not.
Quite often patients can suffer from NERD (Non-Erosive Esophogael Reflux Disease) where they are refluxing acid, but it doesn't hurt the esophogus.
The chronic cough is indicative of atypical GERD (or NERD). Treatment would be PPI therapy for 4-6 months BID.