Having pain in chest, back, both armpits and pain radiates down armpits towards elbows. pain more severe when resting and armpit pain comes in pairs

May be serious: How long have you had these symptoms and how severe are they? If of recent onset and pain is 10 out 10, it is safest to go to the er or even to call 911. If you have had these symptoms slowly progressing over a few months, then see your doctor. Possible causes are broad depending on the rest of your symptoms and exam (aortic dissection, spinal stenosis, cardiac, lung, esophageal).

Many possibilities: There are some different conditions that can cause these symptoms. The history of when it started and how it started and whether there is any associated symptoms such as shortness of breath or racing heart beat would be important. The symptoms could be coming from the cervical spine such as stenosis. It can be muscular though less likely. Certainly heart or lung issues could be causing it too.