Hi, I am a novice to accordion technique so can't help you there. But, I have had finger trouble, and know how worrying it can be. In my case I developed a condition where after a number of years, pain in my left-hand ring-finger turned to stiffness, and then increasingly frequently the finger 'locked'' closed due to inflamed tendons. That led me to do a lot of research into finger/hand pain and in the course of searching for answers I found out a lot from forums, etc. I have since successfully stopped the beginnings of trouble in other fingers, and managed to reverse most of the problems I had for years.
Obviously I am not a medical person, so it is worth getting your pain checked out. But in my experience you are not likely to get much help other than 'it's probably a touch of arthritis, take a paracetamol if it bothers you'.
Whatever the cause of the pain there is a LOT you can do. Firstly - a lot of finger/tendon (and other) inflammation is caused by lack of Magnesium in the modern diet (depleted soil, etc). Unfortunately the cheapest form of magnesium in health food shops (Magnesium Oxide) is not easily absorbed by the body. You could try a few weeks of Chelated Magnesium Glycinate (not as expensive as it sounds, and easily available online) and see if it helps.
Turmeric is very effective at calming inflammation anywhere in the body; as is bromelain (from pineapples). You can add turmeric to food; or you can buy 'medicinal' turmeric and bromelain capsules at most health food shops (I actually got capsules with both together).
Vitamin B6 deficiency can also lead to inflammation and pain. It could be worth trying a good Vitamin B supplement for a time.
A lot of 'finger trouble' forums discuss the widely used 'Glucosamine and Condroitin' - but most people seem to find they don't help.
If the pain is caused by the beginnings of arthritis or rheumatism, and you are serious about wanting to keep trouble at bay, you may want to look into natural means of altering the balance of acid and alkaline in the body. Basically, eating too much acid-creating food (or too little alkalising food) leads to inflammation. Google for lists of acid-creating/alkalising foods. This is science-based, not 'wild and woolly' stuff. Eat mainly alkaline-creating foods for a week or two and you will be amazed by how the aches and pains in your body evaporate.
A simple thing like massaging your fingers/stretching them gently backwards etc can help to keep them moving (but obviously won't stop pain). A great deal of wrist and finger pain can however be caused by over or under-stretched tendons/small muscles. You could search Youtube for very interesting FleXtend exercise routines (FleXtend is an American resistance exercise glove); they use re-balancing routines for specific wrist and hand problems. A lot of grateful people swear by them.
One thing I vowed NOT to do was accept the offered Cortisone injection. I had one earlier in life for a frozen shoulder and it was horrifically painful - and completely useless. I found out afterwards that it weakens the affected joint and certainly should not be repeated if at all possible. I know that maybe for some people it is the best option but I'd have to get very desperate before going down that route. And so many people say again and again on forums that after all the agony, their injection did no good at all...
Well, I hope something here might help a bit. This is in danger of turning into an essay :lol: so I'd better stop now!