Sore swollen grinding knees, what type of specialist should I see?

Rheumatologist. A rheumatologist specializes in arthritis and autoimmune diseases. If you are having pain and swelling you should get an evaluation, to get the correct diagnosis and treatment options.
Orthopedic surgeon. Best diagnosis and treatment plan will be from an orthopedic surgeon or maybe a primary care sports medicine doctor. They will likely get an x-ray.