You're right in your concerns. If, in 3 years, your MD hasn't made a definitive diagnosis either for or against RA, then you need to kick him/her to the curb and find someone else.
I had a similar problem only I looked elsewhere after 9 months (the pain drove me to it). If it is RA, then you need to be on a plan to prevent as much permanent damage as possible. And if it isn't RA, the MD needs to be trying to figure out what it is. Either way, sounds like the place to start is with a different, more pro-active doctor. You're too young to wait around until you have a lot of permanent damage to "prove" its RA.
If it is RA, unfortunately you're probably going to have to suffer the side effects of the NSAIDS, which can be uncomfortable and possibly cause permanent stomach problems. However, they will make it possible for you to get more use from your joints without as much pain.
Good luck! I'll be sending positive thoughts your way.