Hello and welcome to HCM
Pain in armpit while coughing indicates a muscular pain.
Since, you are suffering chronic cough
there must be muscle fatigue
due repeated and continous coughing.
You can use a muscle relaxant
and/ or analgesic balm for the pain.
preparation can help.
However, this is only a symptomatic relief. The cause of chronic cough has to be treated.
Chronic cough can occur in large number of cases.
Get a complete respiratory system examination.
Throbing pain indicates accumulation of pus.
And feeling of numbness is a feature of nerve irritation
Consult your physician as a complete physical examination is needed to order investigations and thus management.
Thanks and take care
Dr Shailja P Wahal