To use "got" in that sentence, you would have to write something like
I got an acceptance letter...
in other words, you obtained something. But your sentence referred to an action by the school of which you were the recipient. Thus, your state of being was changed, and the "to be" verb is more correct:
You were accepted.
While "got" can indicate a change of state as well, as in: I got hot waiting in the sun, I think it is used more for change over time: The more I listened, the angrier I got. If I say: I was hot waiting in the sun, the sense of occurring over time is removed.
Despite your original formulation being very common and likely would have been unremarked, your American friend was correct. In any case, "was" sounds more polished.