Is it on one side or both?

It sounds like you have a tight shoulder causing impingment in the brachial plexus. If you look in the mirror, notice that your shoulders are not level and that when relaxed, you can see the backs of your hands (one side more than the other). Then notice what happens to your hands when you squeeze your shoulder blades together (now you can only see the thumb and index finger - the way it's supposed to be). This is telling you that your posture is compromised and when you fix your posture the numbness and pain will go away. Try these exercises and let me know how it goes:

Matt is right, this sounds a lot like an impingement.

Unfortunatly, its very difficult to tell without an in-person examination, and symptoms like this require medical attention. There is a possibility that these symptoms are due to a much more dangerous reason, and therefore you truly need to seek medical attention for any kind of diagnosis. In a situation such as this, you should always seek professional medical attention from a doctor or specialist whom has completed a full examination. Good luck and I hope you will soon be pain free!

-Sara