I met this guy and I have a feeling that he likes me, but how do I know if he actually does? Why do I feel stupid for catching feelings?

You are certainly not stupid for catching feelings :) You may feel that way because you are not sure it's reciprocated, but that's so normal. You are simply human, and humans catch feelings, and it's an amazing thing. Embrace it. Fear of rejection is also completely normal and valid, so there is no need to feel ashamed or anything like that. Depending on what kind of guy he is, you might try to be more or less direct. Maybe try to ask him out to a coffee? If he agrees, tread the water carefully, and get to know him. Forming friendships never hurt nobody! See where it gets you.