It could be any of the above mentioned problems.

I have arthritis and it sometimes gets inflammatory and causes pain. I use an over the counter arthritis cream and if the pain is bad, just take a few days break from the banjo.

You need to ask your doctor about it, as he can diagnose what it is where we can only guess. Might be something that can be fixed or taken care of with medication, exercise or rest.

As a former teacher/farmer, I'm guessing that plain old repetitive movements might factor into any of the things you list.

Tongue-in-cheek ..... you can't go wrong with the old doc's advice ......

Me: "Doc, it hurts when I __________________ ."

Doc: "Well then stop _______________ ."

Fwiw, I'm having problems with ankles, knees, back, elbows, eyes and ears and  left thumb, but at the moment, my right thumb seems okay........ other than a propensity to pick the wrong string.  

[Yer welcome..... now back to regular programming.    ]

There is a bone at the base of the thumb called the trapezium which I have adjusted numerous times for musicians when it is involved. FWIIW that thumb web area is also where the large intestine meridian starts so you might check your plumbing. So much of older age is about keeping all the pipes flowing.... banjered

First cut out all processed carbs like bread, donuts, cookies, bagels, pasta etc. dont eat processed foods. Give it a few months see if it helps.

white willow bark and turmeric for inflamation.
 

I’d consult an orthopedic hand specialist. My wife had similar symptoms to yours. Turned out to be De Quervain’s syndrome. Surgery fixed it.

https://www.mayoclinic.org/diseases-conditions/de-quervain-tenosynovitis/symptoms-causes/syc-20371332

I was learning, Footprints in the snow out of the D position. After about 4-5 days my left thumb down into my wrist was sore as all get out ! I’ve probably milked more cows than most have seen , but nothing compared to this odd/weird pain I had in my left thumb and wrist area .It took almost a month to get over it. Best of luck. Grab and growl !

Stop picking for a couple days and see an Orthopedic professional for a remedy

I've never seen the inside of a med. school, but my own joints tell me that learning a new tune is much harder on the joints than playing a tune I already know. I tend to allow a lot of tension to build up in my right hand and forearm when struggling with a new-to-me piece of music. I guess I should probably seek counseling for that but it is what it is. I can't really offer any advice because
A.) I'm not competent.
B.) I probably wouldn't heed own advice, thus making myself a hypocrite.
Inflammation is the enemy. Whatever you can do to reduce inflammation will probably help.
Disclaimer:
1.) No med school.
2.) These are the half baked opinions of a rank amateur.
Play the banjo at your own risk!

If your Uric acid level is elevated (routine blood work), your body can form crystals in the bursa sacs lubricating your joints. While those crystals tend to run to lower extremities, they could land anywhere. Immediate pain relief is available with a hydrocortisone shot directly into affected joint. Go see dr, if black cherries or ginger, or turmeric, or pineapple don’t stop attack. If you’re experiencing gout and don’t want needle into the joint, relief will be slower in pill form with Colchicine. While you can only get X amount of hydrocortisone shots per year, I think because it can cause cancer, it has performed miracles in the 7-8 shots ive had. In only one case, right hand middle trigger finger, it did nothing. Colchicine can provide slower relief pill form.