I'm a teacher and I teach at/in school OR at/in a school

I believe you're trying to say where it is that you work and not what it is that you teach.

You have several options, but you'll need either a proper noun (e.g., Jackson Middle School) or the countable noun "school" and an article. It would also be natural to include the type of school (e.g., a high-school or a language school).

A: What do you do?

B: I teach at a ______ school.

When you say "I work (teach) at a school" you make a more general reference to location, one which does not specify that you work inside of the school.

A: What do you do?

B: I teach in a ______ school.

Teachers are in a classroom, and this is going to be what person A pictures in his/her mind.

Of course, the janitor also works at a/the school, as do the secretary and the director, but should each of these workers choose to say "in a school", they evoke different mental images. Person A would picture the secretary in his/her office, the director in his/her office, and the janitor in the hallway (perhaps pushing a mop).

When is there no article?

Teachers are "at the school" but students are "in school" (meaning in class) and "at school", whether they are in class, outside on the playground, or in the cafeteria.

Let's say that someone (A) telephones the janitor, the secretary, or the director:

A: Where are you?

JSD: I'm at work. -or- I'm still at the school.

Only the students are "at school", with no article. Adults work "at the school", with an article.