Acid reflux. When we cough, we rapidly change the pressure in the chest area. The negative pressure created coughing can lead to some of the acids in the stomach being pulled up into the esophagus and the back of the throat. This can cause the burning you are experiencing. Additionally, this may indicate that there is a weak muscle separating the stomach from the esophagus. See your doctor for evaluation.
How long. This going on- is it smoking related? If persistent, see pcp.