I began playing guitar at age 11 (I'm 62 now). In my teens and twenties I played in a lot of bands. At age 31, I was diagnosed with psoriatic arthritis. Over the next fifteen years, the arthritis caused extensive joint damage in both hands and wrists, making it difficult or impossible to play the guitar the way that I wanted to. So, in my mid-forties, I stopped playing guitar entirely, and switched to bass.
In my fifties, I decided to learn to play the drums. I took lessons for about 18 months, learning basic rock beats and fills, and a few rudiments. Then I took a long hiatus from drums until a year ago, when I began taking lessons again. I have a great teacher, and have made a lot of progress in my playing, The damage in my hands and wrists limits my range of motion, and I know I'll never be Jojo Mayer, but that's okay; I'm having a lot of fun, and I'm very motivated to keep learning and improving.
Here's my advice:
1. You don't say if you're seeing a rheumatologist. If not, make an appointment TODAY. Every day that you delay increases the risk that you will suffer irreversible joint damage that may make daily functioning, walking, eating, dressing, etc., difficult, let alone playing a musical instrument. Rheumatoid arthritis can also cause other conditions, such as cardiovascular disease. A good rheumatologist will assess you and prescribe the best treatments for your particular form of arthritis, including drugs, PT, homeopathic treatments, diet modification, exercise, etc. Biologic drugs (Enbrel, Humira) were the only thing that stopped my arthritis in its tracks, but they came along fifteen years after I was diagnosed. Today there are many more treatment options available to you.
2. Find a good teacher who emphasizes tension-free hand technique. If you start out with improper hand technique, you can do more harm than good. If you can't find anyone locally, look into Skype lessons with Bill Bachman at drumworkout.com.
Hope this helps. Good luck and welcome to drumming.