I had something similar, but it was less of a continuous pain -- more of one that came on when I elevated my arm. It turns out that I had developed some bad habits when lifting or raising my arm. Basically, I was using the muscles around my neck (trapezius) to "lift up" instead of using my lower back / shoulder blade muscles to "pull down". It caused my shoulder joint to rotate improperly and it pinched some tendons in my shoulder as I lifted. It also was aggrivated at night. I separated my shoulder many years ago and suspect this bad lifting motion may have been started by this.
The good news is with about 4 weeks of physical therapy where I got "retrained" on how to move and strengthened my lower back muscles, the problem is pretty much gone.
My husband had the same problems in his shoulder from years of heavy lifting at work,his back was in a pretty bad way too.
A friend of ours introduced us to a product called Monavie.Not sure still why it worked but his back and shoulder,in his words have not felt this pain free in years.
The friends website is http://www.mymonavie.com/knight06
Good luck if you give it a try.
You need to see an orthopedist. A general doctor cannot diagnose a rotator cuff tear (well, maybe if they do sports medicine) effectively. You will need an xray done of the shoulder. If the ortho suspects a tear, he/she will probably order an MRI. You need the ortho to "read" the xray. Radiologists that normally "read" an xray look for different things than an ortho does. If you have already taken xrays, take them with you. The ortho may order new ones to compare if the ones you took are older than a week. If you don't want to do this and still want to pursue the nerve theory, you can go to a chriopracter. They can evaluate the shoulder for a pinched nerve and give you a manipulation to relieve that. If this doesn't "do the trick" then go see an ortho. good luck