Rheumatoid Arthritis Support Group
Rheumatoid arthritis is a chronic, inflammatory, multisystem, autoimmune disorder. It is a disabling and painful condition which can lead to substantial loss of mobility due to pain and joint destruction. The disease is also systemic in that it often also affects many extra-articular tissues throughout the body including the skin, blood vessels, heart, lungs, and...

With regards to the rash, don't discount developing an allergy. I was on Sulfasalazine for 6 months and had no problems. I started getting an itchy rash about 11 am, So I would take a Benedryl and it would clear up. This went on for 2 months, before I realized that I was allergic to Sulfasalazine, but I wasn't getting the reaction for 2 hours after I took it, because it was enteric coated. But I did have 6 months where I was allergic.
JMHO. You need to broach this topic next time you see your rheumatologist in August!
I have no idea if being allergic to MTX is a thing, but you should definitely keep an eye out for a pattern ...
Also sounds like you need to hold the reins in a manner that don't affect your fingers.
While it's true, as Marlene wrote, that it could take a while for an adverse reaction to occur, I doubt you're having one. The sunblock wears off in the wind, you burn, you develop a rash from the sweating. As for the finger, if I understood correctly, this is your own doing by the way you ride.