Distribution along the arm and involving certain specific fingers could mean it is a C7 nerve root problem from the neck. If this is the case besides pain there could be sensory disturbance (burning, tingling, pins-and-needles) or weakness (possibly grip or triceps weakness).
If any of this is true for you then the source of the problem needs to be localized, and there are a few possibilities, which cannot be sorted adequately over the internet.
Since you sit at a computer many hours a day one possibility is a nerve compression related to ergonomic position. If this were due to a cervical compression (where the nerve root exits the spine in the neck) then perhaps changning position so that your neck was straighter or in some more "neutral" position might be helpful. Consider seeing a neurologist. Good luck.
Yes, an ortho can be just fine, if he/she will look at this possibility with you.
It would not be appropriate, in my opinion, to recommend exercises - that is, treatment - when the diagnosis is still not known. I think it is important to first know what is wrong, and then decide on the best way to treat it. I mentioned the ergonomic issue simply because it is simple, you had defined your long hours at the computer as possibly relevant, and it doesn't involve a formal treatment program. I think your best interests are served by first trying to know what specifically is wrong. Sometimes ill-advised treatments may make the problem worse.