Good for you.
I don’t think you need to describe the whole incident with your friend. Maybe something like
“I was disciplined at school after acknowledging that I had consumed alcohol prior to arriving at a school event. This was a one time event, which I regret and won’t repeat. “
I’m not an expert here but I just think super short and to the point of what you did and that you won’t do it again. It was wrong. Don’t over blow it, don’t do it again.
The fact that the school doesn’t report it will further underscore that they don’t view it as a major incident.
Good luck.