I had that problem (it also radiated through my entire arm) but it was due to too many airborne ops and landing on that shoulder. The injury damaged some nerves and it affected my left hand and arm. I noticed a few years later that when I would life heavy it would bother me more. I went to see a physical therapist and they gave me some rotator cuff and shoulder exercises to stabilize it. It worked.
Also, it could be a C6 or C7 vertebra problem (I cannot remember which one it is) but I know there is a nerve that runs from C6 or C7 that goes to the hands and if that nerve gets pinches it can cause problems. I got hit in a car accident and this triggered the nerve. Exercise worked out that kink. If you are seeing a chiropractor then I doubt it is a vertebra issue.
This site gives an overview of some of the exercises I did - they were not the traditional dumbbell press / lateral raises etc. (the normal BB exercises we are all used too). They all involved no weight (or very low weight). It is amazing how the little exercises can make a difference with injuries.
http://orthoinfo.aaos.org/booklet/view_exercise.cfm?Thread_ID=19&topcategory=Shoulder
Good luck.