First of all, keep in mind that I am unable to diagnose you because I am unable to examine you, this forum is for educational purposes.
Pain in the shoulder with limited range of motion, is likely due to a joint related issue such as frozen shoulder or arthritis. I would recommend that you see your family doctor to evaluate your arm. This condition can occur without a prior cause, but is most often due to lack of use related to a previous injury such as tendinitis, bursitis, stroke, etc. Treatment is physical therapy and possibly corticosteroid injection. Plain Xrays or an MRI can be used to evaluate for other causes, but are not needed for the diagnosis of frozen shoulder.
I hope this has been helpul.
there are many nerves that run through and around the shoulder. when the shoulder joint is out of whack, it is understandable o have symptoms down the arm. It sounds to me like a muscular or perhaps a muscular/orthopedic issue. Did you overuse the shoulder in athletics or do you hunch over on the computer? I had this same problem and I fixed it on my own w proper stretching/trigger point release. But you should see a shoulder specialist to rule out any rotator cuff/labrum tears. if there is nothing obvious on his exam/tests (MRI perhaps) then you'll probably be referred to a PT.