osteo arthritis is most common in the thumb and its rarely seen in anyone younger than 40 or so. it is degenerative changes at the articular cartilage and it takes years and years and years to develop. rheumatoid arthritis is seen in elderly people and is most common in women and is rarely seen before age 65. it is characterized by the deformity of angulated joints in the fingers so without that deformity i can assure it is not RA. if it was gout you would know it, they would be very red and swollen and extremely painful to move or touch. this is because the uric acid crystals attack the joints causing severe pain. gout is seen mostly in major weightbearing joints like the big toe or the knee and is unlikely to be caused by guitar playing.
it depends on where your symptoms are. in our office we see things like tendinopathy from overuse which can resulf in things like trigger finger. if it is a true trigger finger there will be a painful catch in the palm side of the fingers when they are flexed beyond 80 degrees or so so if you are getting a painful pop you should see your MD. it is most likely a tendinopathy issue that can be treated with consistent stretching of the intrinisc muscles of the hand and fingers both before and most importantly after playing. you can also treat it with icing about 20 minutes a few times a day as needed, you can also try some over the counter anti-inflammatories such as 600 mg advil or ibuporfen 3 times a day or 500 mg of aleve or naproxen twice a day. most importantly, you should probably rest the hand for a week or two and avoid pain causing activities and repetitive activity like guitar playing. you will not lose your chops by resting from the guitar for 10 days or so.
if you are not having any numbness or tingling and painful popping or lost range of motion you are probably ok. guitar playing can cause some serious problems and ergonomics is a big reason why. i know that i developed a large ganglion cyst in my wrist (olive sized) that had to be surgically removed so now i am much more careful about how i play.