Hi Alyssa,
It's not your fault. It was an accidental thing that could happen to anyone. You are still the vegetarian you were the day before this happened. You didn't do anything wrong.
Regarding people telling others... I would hope they wouldn't say much, as they would hopefully have other things to talk about. However, realistically, they might. BUT, your reaction could impact their reactions. I would recommend trying to play it cool as much as possible. I don't know if that will work, but it seems like when something upsets someone, it becomes more interesting for others to discuss sometimes. I am socially awkward, so I don't have any tips on what to say. (Sorry about that.) But I would probably lean in the direction of not making a big deal of it (to people at school) and it will probably blow over pretty quickly, if it hasn't already.
Alyssa, you didn't do anything wrong. A few chips (or a bunch of chips one day) with chicken fat that you didn't even know was there doesn't mean one bad thing about you. You are doing excellent things for animals and for the environment by being vegetarian. Some chips one time do not change that. I know I have made mistakes before (though no one talked about it to my knowledge - how frustrating it would be for people to do so). Would I be freaking out? Yes, I admit it. But you can hold your head high knowing that you would not intentionally eat something with chicken in it, or any other meat. For the records... Who puts chicken fat in chips anyway?! I have never heard of that!
I hope you feel better. I can see why this bothers you. It sounds really upsetting. But you have nothing to be ashamed of. Good luck at school tomorrow. You can do it. You've got it!