There are some blood tests that show various things, however they do not always show positive even if you have the disease. If you look down the posts here, there is one called "do you know what these blood tests are..." or something very similar to that. Erin has written a response discussing the various tests and what they can show when checking for RA.
You don't have to have the extreme swelling and redness to have arthritis. I'm sorry to hear you are dealing with so much, I wish you the best in getting relief.