Definitely agree with ggreg. Absolutely! I am going through the same things right now with arm/neck/back pain. I have C4-C5 herniated disk without cord compression.
Some physicians will state that should not cause problems but I beg to differ.
Well, assuming you have a bulging disk in your upper back or neck area, yes, your arm could indeed be bothering you from that! A disk will bulge outward and there are a bunch of nerves that come out from the spinal cord and go to other parts of the body, and any of that can be pushed on and will cause a distal part of the body to hurt. Plus, when a disk bulges, it'll sometimes cause inflammation and swelling, and that, too, can cause those same nerves to misfire and hurt other places in the body.
Go online and do a general search for something like "anatomy illustration spine nerves" and you maybe can see some pictures of how the nerves come out from the spine and you'll understand how come a bulging disk in, say, the cervical spine will cause the arm to hurt. Or you can do a search for "bulging disk nerve pain," and you can read articles about the situation. I hope this helps you understand what is going on.