HI, thanks for using healthcare magic Persistent coughing is most commonly related to post nasal drip, asthma and GERD (gastroesophageal reflux disease). Post nasal drip is the most common of these three. Some persons may have a silent drip where they are not aware that of the drip and only present with symptoms such as coughing. It is treated with topical steroid nasal sprays, avoiding trigger factors if known and oral anti histamines. GERD is also a cause to be considered. The normal x ray rules out more serious causes such as cancer. I hope this helps