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Phoning home? Should I know my place?

We seem to have stomach bugs and covid resurfacing at work and we’re on skeleton staff. Limited SMT available in an emergency. Today they were near enough all out. An incident took place between two girls who were fighting. One ragged the other ones head and smacked her. Call her student A
The student injured student (student b) hung back after school and we filled in the incedent report as usual and was visibly upset. Took the statement. Did the procedure. Well not me but others did.
So, student A was already being a bit silly at the start, so I rang home and said “your daughter wasn’t following rules from the start of the lesson. I also wanted to alert you of an incident that took place at the end of the day whereby they physically hurt another student. I will be escalating it and you’ll hear from the school in due course”
Later on I sat back and thought “was that my place” bare in mind we had 0 SMT today. They’re basically all ill and one who we had left very early
Was this above my station? Should incidents be dealt with by designated staff only?