For 3 days, the skin on my left inside upper arm is extremely sore and burning. there is nothing like redness or rash. don't know how to treat it?

The information provided is not enough to make a confirmed diagnosis. Burning pain can be indicator of nerve involvement, differential includes Shingles(pain can start 24-72 hours before the rash appears and sometimes unto 7 days, so watch out of developing rash), other condition to be further evaluated is nerve entrapment which can happen in the neck( osteoarthritis), peripheral neuropathy.