Learn English – How to express a feeling beyond proud

The word "embarrassed" is used by native English speakers in exactly the sort of situation you describe. "I felt embarrassed for them" implies that you are certain the other person is doing or saying something embarrassingly wrong and that they would be embarrassed if only they knew!

This answer refers to American English, I expect it's different in the UK (and perhaps from one UK country to another).

If someone is in elementary, middle, or high school, we usually ask

What grade are you in?

and the answer would either be a number grade First grade through Twelfth grade, or a high school student might answer with freshman, sophomore, junior, or senior (when I went to school 40 years ago, grades 7-9 were often junior high school, so freshmen didn't usually identify themselves that way).

If they're in college/university, the question is usually

What year are you in?

and the answer would be freshman, sophomore, junior, senior, or graduate school.