My mother in law's arms get numb and her fingers swollen why is that?

Many possibilities. Her doctor is the best person to figure this out. Problems in the joints, nerves, or blood vessels may be causing these symptoms. A primary doctor or rheumatologist may be helpful. Rheumatologists diagnose and treat joint and musculoskeletal conditions.
Possibilities. There are various possibilities but the list includes a blood clot in the vein returning blood from her fingers to her lungs and infection. Both are serious. Please have your mother-in-law checked out today!