HI, thanks for using healthcare magic
The x ray would rule out infection or a lesion in the chest though if the coughing persists despite treatment then further imaging such as a CT scan may be needed.
The most common causes of a persistent cough are: (1) post nasal drip- this is the most common cause and there are some persons who are not aware of the drip itself but only present with the cough
(2)GERD- reflux is also common , again the typical symptoms of reflux may be absent (burning pain,
bloating, regurgitation)
(3)asthma
(4)non asthmatic eosinophilic bronchitis
Since post nasal drip is the most common reason, it is usually treated first unless there are obvious signs or history of one of the other causes.
Treatment involves the use of an anti histamine/decongestant combination (eg zyrtec d,
allegra d, claritine d,
benadryl d) along with a
topical steroid nasal spray (eg nasonex, nasocort, flonase).
These have to be used consistently for 2 to 4 weeks, the response can take weeks to occur.
Some persons may have more than one cause eg reflux plus the post nasal drip
I hope this helps