Its probably rust
Im not a doctor so don't rely on this but it might be lack of blood flow or something simple like water
Try stretches after or before a session (make sure you know the benefits and drawbacks of each) and also make sure your posture is good (im not sure about 6k but 4k posture is best described by looking at wonderosu's 99.96 ooparts play)
There's so many things that can go wrong but as long as your pain is a burning feeling your fine and overtraining is EXTREMELY hard to do so only worry about that if your playing an unbelievably high amount every day which would lessen even more with 6k having a more reading focused playstyle
My conclusion is your either fine and need to get back into shape or have some kind of lacking like malnutrition bad posture or going too far too fast if you want a good answer just go to your doctor or a hand specialist and ask them for advice on how your hands work im merely speculating and could be worsening your condition