How To Treat Chronic Cough Leading To Stinging Sensation In Chin And Lower Jaw?

Hi, I've had a really bad cough for years, I assumed that I picked it up from second-hand smoke or something. I'm not looking to treat it, but when I cough repeatedly, my chin and lower jaw stings, and stays that way until a few days later. What's new, I just moved to a place with a lower temperature, is that this happens when I'm out walking; I breath in and they sting again. Is there anything that I can do for the pain? I don't know of advil is going to be of much use. Thanks!