I recently had a patient who had a broken ankle and wrist following a serious car accident. While we were working in the clinic, the patient kept referring to her ankle as the "bad side." I kept calling her injured ankle the "affected side." In general, physical therapists usually refer to the injured side as the "affected ankle," the "surgical side," or the "injured wrist." We try not to call anyone's body part "bad."
Technically, your body part belongs to you, so you can call it anything you wish. If you want to call your broken arm the "bad arm," that's completely fine. But your PT should shouldn't call it "bad."