English Grammar - I am at school and I am in school which is correct?

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My line of work brings me joy ,especially when I know I can inculcate knowledge.
When it was time for recess at my place of work,two of my fellow teachers, Harrison and Joe came to me, they said there was a question they wanted me to sort out for them and I agreed to help them out. Joe asked me a question:
I am at school and I am in school which is correct?
After asking the question Harrison told me they decided to ask me because I am a phonics instructor so they are relying on my answer. Well I wasn't expecting that question but this was my reply:
I am at school is British English while I am in school is American English.
Both are correct.
AT shows presence or physical location.
When I say I am at school it means I am inside the school premises or grounds. I don't necessarily have to be a student to be at school, parents can be at school when they accompany their children to school.
I gave two example sentences,

1. I have been at school since 8 AM .
   (that means I have been inside the school premises or grounds )
   2.I was at school with my child.
   (that means I have Been inside the school premises with my child)
   IN shows during or actively doing something.
   When I say I am in school it means I am receiving tutoring or I am learning. I have to be a student to be in school even if it via online tutoring or learning.
   I also gave one exams sentence,
2. While you called I was in school so I couldn't answer the phone to avoid being distracted.
   (that means I was being taught while the call came)

I am not an English teacher but being a phonics instructor makes me abreast with English language and they were pleased with my answer.
I was happy I could inculcate knowledge not just to children but to adults too.
Thanks for stopping by!! 😊