It is uncommon to have neck pain due to TMJ problems, as the muscles involved are all connected and go from your face to the neck and the shoulder.
I also strangely suffer from back pain in the subscapular area by the shoulder blade. and up to the neck.
I know that my posture is not that good. My neck has a tendency to protrude forward. I also have clicking in my right shoulder. I am thinking that couple traumas caused it.
Have you had any previous car accident, neck or shoulder injury?
Working by the computer also makes my pain unbareable in the neck and upper back on the right side although I am left handed, but I use the mouse with the right hand. Since no longer working with the computers that much, I am seeing improvement. It is very important to sleep with the bach and neck straight. Best position I found is one on the stomach, this way the neck is forced back. After long day when I lay down in this position I feel tingling in the lowest part of the back, like electrical kind of sensations when I try to relax.
I would also recommend a TENS unit, (Transcutatnous electrical stimulation), have you tried it with physical therapy? It helps me when the pain is very bad. Also the capcaisin cream/liquid roll on helps me too.
Please tell us what physical therapy you had?