Tingling in a limb almost always means a pinched nerve or inflammed muscle impinging on a nerve. Sounds like in your case it may be in your shoulder or neck somewhere. Try putting a pillow under your elbow when you are typing to take weight off the shoulder area and see if that helps. You might also try cold packs and motrin or advil for inflammation.
If this doesn't help, then I suggest a trip to the doctor for further testing.