You can have a rheumatoid panel done. It measures rheumatoid factor (which is not a 100% guarantee you have or will have RA) and various inflammation markers. Your PCP can order it. They might be hesitating because you can have RA and have no rheumatoid factor (called seronegative RA), and I know you can have normal inflammation markers and still have active RA as that is what happens to me. If all are positive, it might help get you into a rheumatologist sooner. You can also ask to be on their cancellation list, if they have one.
If you haven’t had one, I strongly recommend a thyroid panel. Hashimoto’s thyroiditis can present with your symptoms. So can menopause.
As for how to deal with pain in the meantime, heat usually helps, and CBD cream (with THC if it’s legal where you live) are noninvasive ways. Your PCP could prescribe an anti inflammatory such as ibuprophen and naprosyn, which you can get over the counter but the prescription version is more powerful. Aspirin might help.
Some people like warm wax treatments on their hands. I’ve never tried it as I just wrap a heating pad around my hands when I need it.
Best of luck, and I’d be glad to answer any other questions you have. I had Hashimoto’s diagnosed in 1992 and rheumatoid arthritis diagnosed in 1998. So I’ve been around the block on the autoimmune stuff.