That sounds very similar to what I had some years back - little finger, ring finger and outside of middle finger of right hand plus the outside of the right forearm. It turned out to be a cervical spine disc problem which was kicked off by a sneezing session.
Certainly not life threatening but definitely worth further investigation.
However, in my case it took three GPs and a Neurosurgeon before it was correctly diagnosed so be sure to persist until all avenues have been checked and you're happy with the diagnosis.