The RF test alone is not enough to differentiate Lyme from RA - and the treatments are completely opposite, as for RA it's all about
lowering immune function and all the meds will say to make sure the patient doesn't have an active infection - something most doctors miss.
For Lyme it's all about
treating the infection(s) and raising the immune function to help it fight this as well. There are a few unlucky souls that end up with an autoimmune issue while they have Lyme and it takes a well organized and cooperative group of doctors to help them the most.
The testing for Lyme is not very specific, as the current testing relies on the amount of antibodies produced by the immune system. The problem is that Lyme lowers the immune function, so many can't produce enough antibodies to test positive, even though they have the infection(s). i was one of those people and didn't test positive until I had had a full 12 months of treatment for Lyme. This is not uncommon.
Unfortunately, without a Bull's eye rash, or a positive test, there is no other way to get concrete proof that you, or any of us, has Lyme - other than trying treatment and watching for the usual patterns that Lyme produces during healing and eventual healing/improvements.
Keep searching for your answers, as I said the two conditions need opposite treatments. Push your Rhuemy to do more testing for the RA to begin with. There are several other tests that can still be done, although some of those tests can be positive from Lyme as well:
www.webmd.com/rheumatoid-arthritis/tc/rheumatoid-arthritis-exams-and-tests