Haven't been here in awhile, but just saw your post and thought I'd respond.
I'm 56 and returned to rudimental drumming after a decade hiatus.
I deal with daily hand stiffness and pain, with occasional knuckle "lockup" on my left hand (those barre chords, you know?)
I soak my hands in a bowl of hot water every morning for ten to twenty minutes to reduce the stiffness and it does help.
I now make my living as a touring singer-songwriter and music educator, and figured playing guitar every day would already reduce potential hand issues.
Boy, was I wrong.
Drumming has made things worse.
So I've had to decide how much drumming I can handle and still have enough left in my hands for paid musical work.
I play occasionally in a community marching band (when I'm not touring), and that is about as much drumming as I can handle for now.
I'd try soaking your hands in hot water in the morning, using some kind of menthol-based joint lotion (don't rub your eyes), and if it's really bad an occasional tylenol wouldn't hut. If it stays the same or gets worse, see your doc about ppossible advancing arthiritis. Good luck!
Beth