Hi and welcome to HCM. Thank you for your query.
I dont think cough is related to this. This sounds more like it could be the beginning of perianal abscess
or some subcutaneous lesion. YOu need to do proctologist
work up to exclude abscessus which should be terated by surgical incision and drainage
. If this is just subcutaneous lesion such as lipoma,fibroma
or ateroma then it doesnt need to be treated unless this is cosmetic problem.
Wish you good health.