I have chronic left knee swelling and pain (for 3 years!) after extensive testing diagnosis is synovitis. Any recommendations?

Injection or surgery. I'm assuming after 3 years you have tried pt and antiinflammatories. Draining the knee followed by a cortisone injection (assuming the fluid doesn't look infected) could help. If there is any suspicion for infection, hold off on the cortisone until the synovial fluid has been evaluated. Last resort is to see an ortho surgeon about a synovectomy.
Depends. Depends on type of synovitis- if no tears etc, arthroscopic synovectomy works well and also biopsy the synovium to check for diseases like rheumatoid and PVNS.