What causes swollen wrists with pain as well as swollen ankles?

A number of possi--: Bilities, including rheumatoid arthritis due to the bilateral involvement of multiple joints; other types of arthritis. Sometimes viral infections can cause multiple joint swellings/pain. Need to see pcp for onward referral to a rheumatologist, who can diagnose/treat such conditions. You needs xrays, labs and likely joint fluid to help aspiration to DX or rule out other diagnoses. Good luck.

Swollen joints: You may have an inflammatory arthritis. Check with your doctor and get some specific blood test.