Definitely appeal the decision and if that fails, go to a tribunal. I can't praise Benefits & Work website enough for their downloadable guides to claiming DLA and other benefits. I'm sure its thanks to using their methods of completing the claim form that I was awarded full DLA in just 8 days.
Whilst you're waiting for the reasons why you were turned down, could you be looking at your application form again (hopefully you kept a copy) and see if there's any more info you could have included? As an example, I enclosed 9 additional type written pages to give a potted 39 year history to support my application, some parts were repeated, but don't worry about that as that's the way the form has been drafted. The important thing is to make the form fit your RA & any other health conditions, rather than trying to make your health condition fit their form. Also if some of the tick boxes don't fit your situation, don't tick any of the boxes but explain in detail on additional sheets.
If you haven't done so already, ask your GP, physio, O.T., carer, Rheumatologist, Surgeon, employer, ex-employer, friend or family member, basically anyone else that knows you well to write a letter or report in support.
The more info you give to show the assessor how RA symptoms (and any other conditions) affects you, what drugs you take, effects of drugs, how often you see health professionals, what tests you've had, whether you've seen a surgeon to discuss surgery options, had surgery, the outcome of that surgery, etc. etc., its less likely you'll be asked to have a medical, asked for more information, or a visit from Social Security etc. Plus, the more detail you give, the less likely a Tribunal will be able to turn you down.
Good luck!
Carol