Did you have any injury
? if yes then u need to go and get an X-ray taken, it could be an injury to the ribs.
If no then let us know if you have any fever, as the next possible reason for chest pain
and cough would be a chest infection
. However, this would not interfere in the movements of your arm, as u have mentionedand unlikely to be present for a m onth without worsenning !!
So the best option for u would be to tie a band around your chest and give some hot water fomentation and take Tab Diclofenac
50 mgm 8 hourly with Tab Omez 20 mgm 1 tab at night. for a day and if there is relief should consider an X-ray.