Reflux of stomach contents reaching your neck and windpipe are the likely cause of your cough. Please see the section "General Therapy".
Initial therapy should include simple remedies to prevent reflux from occurring. These include no late meals (after 7 p.m.), avoid rich foods in the evening, avoid alcohol and chocolates before bedtime. In addition elevate the head of your bed to at least 30 degrees to let gravity keep your stomach contents down. Over-the-counter stomach medicine and antacids are probably not beneficial at this point. For more severe cases prescription medications to prevent stomach acid and tighten the esophageal sphincter are very useful.