If it's in your middle, ring and pinkie, and up into your elbow area there are a few possibilities. You could possibly have ulnar nerve impingement near your elbow, or a subluxating tendon (snaps over the nerve and snaps back into place, thus irritating the nerve). Or it could be higher, up into your shoulder, which is a little more likely since you said it is three fingers, instead of just your pinky. You could have impingement syndrome in your shoulder due to the way your bones are formed, or movements of the musculature. It could also involve your brachial plexus (the same thing that is irritated in "stingers" or "burners"). Finally it could be radiating from your neck, since your nerves originate there. You could possibly have a cervical disc bulge, or something else irritating those nerve roots.
As you predicted, go to a doctor...but not an internist, or a family practitioner. Go to a good musculoskeletal doc, (orthopedist or osteopath) or a chiropractor, they'll be able to diagnose you effectively and do the tests to rule out these possibilities. If you don't go to a chiropractor first, and the doc says it is your neck, and you need surgery, go to a chiropractor for a second opinion, to check to see if they can keep you from it.
Certified Athletic Trainer, and in my second year of chiropractic school