There is specific criteria to diagnose fibromyalgia. You have to have 11 out of 18 of the tenderpoints, pain above and below the waist and the pain has to be present for so many months. This is why you need to see someone who specializes in this. Otherwise, many physicians just give out this diagnosis without a proper exam because they just don't know what it is or how to diagnose it.
If that's it for symptoms then it's not FM. It's too localized and is probably a specific soft tissue or other injury (or repeative injury from a certain use.)
However, if it's as though you're back just won't clear up with no other explaination, you may want to look into myalfacial pain syndrome which tends to be upper back, with trigger points, and is more limited a set of symptoms than FM. (Not that's it's not sometimes extremely painful and incapacitating.) I'm not spelling it right. There's a book that comes with a tool, a stick with knobs on the end, to push the points yourself that someone told me was a god send. If I ever remember the name I'll come back and type it.
Debby was right though to make sure to include your other symptoms since then it may well be FM.
I also have trouble with my right shoulder but I also have pain in other areas? Do your muscles ever hurt anywhere else? Ever feel like your getting the flu? Stay tired? I went to a specialist to find out if I had it. Mabe your Doctor should send you to one for evaluation.