Wellbutrin can cause numbness and tingling of the extemities and around the face. It is not one of the more common side effects, and you should address this with your doctor. If the Wellbutrin is found to be the culprit your doctor may switch you to another medication. Do not stop taking your wellbutrin unless your doctor instructs you to do so.
Yes, side effects can occur at any time especially when new meds are added to the mix however, there could be other causes including diabetes or other endocrine disorder, some type of spinal injury or neuropathy, and sometimes even a vitamin B6 or B12 deficiency can cause tingling in both right and left fingers. Ulnar Tunnel Syndrome (which is pretty much the same as Carpal Tunnel Syndrome except it affects the ulnar nerve) can cause the little fingers to have numbness and tingling.
Because these symptoms are new and you have been taking the Wellbutrin for so long, I suggest you have your doctor investigate the definite cause and rule out some of the above possibilities.