There is a mole on my back. A surgeon told me its not melanoma. Around it there is pain and it causes pain to my right arm too. Infection?

Need exam. Now that you know what the mole "isn't", i would ask him/her what it "is". It sounds like you are have enough symptoms to warrant removing the mole and examining it under a microscope to see what it is. An infection should cause the skin to turn red, with swelling, and pus drainage.
Possible. It is possible that it is an infection, but impossible for me to tell you without an examination. If you have concerns regarding your skin, the best person to see is your friendly dermatologist.