Is it rheumatology the specialty that deals with arthritis and stiff joints?

Yes. A rheumatologist can help you with arthritis and stiff joints.
Yes. However at some point another specialist or surgeon may be needed such as a podiatrist or orthopedic surgeon especially if you need surgical intervention on a specific joint.
Yes and immunology . Yes we are the medical arthritis doctors - a branch of internal medicine. We help diagnose arthritis syndromes and develop treatment program. We are often asked to evaluate complex medical problems.