One strong possibility is of a spinal cause like spinal disc herniation or prolapsed especially at the cervical or thoracic level of the spinal cord. This causes neurological pain which can radiate in the forearm and lower part of the body also. This is an important possibility because the nature of the pain is burning and radiating. You should consult a neurologist as well as an orthopedician and get MRI spine (cervical and thoracic levels), MRI of the left upper back and shoulder blade (for any soft tissue injuries) and electromyographic studies and nerve conduction velocity test done. Till that time, apply warm compresses and some topical anti inflammatory analgesic creams on the back. Once the diagnosis is confirmed, specific treatment can be started.
Hope it helps. Take care and do keep me posted on how you are doing. Warm regards.