It would be difficult to say if it were neurological.

I'd try Salonpas patches (the original ones with methyl salicyclate in them). You can cut them to wrap around your fingers, leaving the knuckles free to bend.
These are at WalMart, RiteAid and Costco.
http://www.iherb.com/Salonpas-Pain-R...FcJQ7AodfUYAjg

It is important to get the correct ones, as there are many other forms.

I use them all the time for the arthritis I have in my hands and feet too. They are inexpensive and work well for most things.
Some hand pain can be tendonitis too. These will work for them as well.

I also wear wrist splints at night. This one is quite comfortable and affordable (at CVS these are over 30 dollars each).

http://www.amazon.com/Futuro-Energiz...ro+wrist+brace

These wrist braces worn at night protect your hands from bending and compressing the carpal tunnel. This model I've had for over a year and compared to others is the most comfortable.

I've worn braces at night on and off for over 30+ yrs. They can really help.

These are two over the counter interventions that may work for you. I still use them as my hands seem to go in flares and improvement still today.