I have chronic coughing and it does bother me as it hurts my back when I cough, due to having a herniated disk in lower back.?

Possible. Back pain that radiates to leg and lancinating that is worsened by coughing or strining is suggestive of a herniated disc physical therapy, and other modalities are vailable see your family doctor to havre it further dealt with.
Chronic cough. The problem is really why do you have a chronic cough. Are you a smoker or do you have asthma or bronchitis or copd? It is most advisable for you to see your doctor for an examination to determine why you have a chronic cough and then receive proper treatment.