Poor nutrition will lead you do developing joint irritation. I often recommend that people with joint pains begin taking Essential Fatty Acids, such as Borage oil and flaxseed oil daily to help their bodies regulate the inflammatory response better. Secondly, I recommend glucosamine sulfate for joint pain conditions. This is a substance found in cartilage and helps to rebuild the joint surfaces. The second avenue I would look into is the health of your nervous system.
Joint pains can result from irritated nerves from the neck.
The joints receive their nerve supply mostly from the radial nerve - which stems from the lower neck. Think back to any neck injuries or previous neck complaints. A chiropractor can easily determine if this is a problem that can be initiating your finger pain. The third thing to look at is your playing style itself. Sometimes simply playing with less force can reduce the irritant to the joints and thus reduce the swelling and pain that follows.