My mom can't move her shoulder/arm for a few days. Is that called frozen shoulder?

No. Frozen shoulder takes many months of pathology in shoulder for it to become frozen. Have it checked by an orthopedist, there are some with special training and vast experience in just shoulders. Or see sports injury doc.
Frozen shoulder. There are 2 main causes of shoulder pain and stiffness, or true loss of shoulder motion. One is frozen shoulder, the other osteoarthritis. They can be differentiated by simple xrays. Most commonly, patients have difficulty due to pain, but do not have true "stiffness". If the loss of motion persists, see an orthopedic surgeon for evaluation. Good luck!