Burning back pain between the spine and the right shoulder blade. The pain extends through the right shoulder and down the right arm and elbow.

This is a fairly . Classic pattern for a lower cervical disc herniation such as c6-7 level. Sometimes a shoulder problem can present like this as well. Rarely, a lung issue (pancoast tumor) can present this way. If it does not improve with time or worsens, see your physician.
Myofascial Pain. If you are having a lot of stress, bad posture, weak muscles (muscle imbalance) then this may be secondary to myofascial (muscle pain). If the pain down the arm is shooting-like and associated with numbness and weakness then it might be a herniated disc pinching a nerve in the spine. Visit your doctor for an evaluation, imaging and treatment as needed.