Originally Posted by mrsD

If the joints affected are the first metacarpal joints at the palm...that indicates Rheumatoid arthritis. Should have a doctor evaluation to prevent further damage. RA erodes joints away.

If the swelling is at the first joint (distal) at the fingernail area, those are Herberden's nodes, and indicate Osteoarthritis, and this is less critical.

I use Salonpas over the counter for stiff fingers and toe pain.
You can cut them into strips and wrap around the finger.
Stiff fingers may be a prelude to "trigger finger" where the tendon gets stuck. So I prefer to use the Salonpas often to help prevent this, because it requires surgery to release.