Is there such a thing as an acid without a hydrogen? I'm in AP Chemistry and we are learning about the Brønsted-Lowry model and my teacher mentioned that "for the most part" acids have hydrogen, could there be such a thing as an acid that has no hydrogen in it?
It depends on which definition of acids and bases you are using. 

According to the Arrhenius theory, acids are defined as a compound or element that releases hydrogen (H+) ions into the solution. Therefore, there are no Arrhenius acids without a hydrogen atom.

According to the Brønsted–Lowry acid–base theory, an acid is any substance that can donate a proton and a base as any substance that can accept a proton. Hence, there are no acids without a hydrogen atom according to this theory.

But according to the Lewis theory of acids and bases, an acid is any substance that can accept a pair of nonbonding electrons. In other words, a Lewis acid accepts a lone pair of electrons. According to this theory, acids without a hydrogen atom can exist. (A coordinate bond is formed between the Lewis acid and base. The compound formed by the Lewis acid and base is called a Lewis adduct)

A great example of this would be $\ce{BF3}$. It is neither an Arrhenius acid nor a Brønsted–Lowry acid but it is a Lewis acid. The boron atom accepts a pair of nonbonding electrons from another atom or ion to complete its octet. Here $\ce{BF3}$ is a Lewis acid as it accepts a pair of nonbonding electrons. 



The fluorine ion here is a Lewis base as it donates a pair of electrons.

If you want to get more rigorous about the definition of Lewis acids: "a Lewis acid is a type of chemical that reacts with a Lewis base to form a Lewis adduct".

More about Lewis acids and bases here.