First, and most importantly, don’t believe what they say about you. This is crucial. Small people bully and mistreat others. Their words and their actions do not and should not define you.
Self-confidence, knowing who you are, and believing in yourself are the keys to taking the teeth out of bullying. Often, bullies will stop when they realize that they aren’t getting what they want, which is an emotional response from you. It also makes you less likely to be bullied in the future, because the type of people who bully others tend to sniff out insecurity.
I know you don’t want to tell anyone, but once bullying gets to the point of posting negative things on social media, you need to tell someone. Insulting you to your face is one thing. Gossiping about you to others is also common, but once you put something in writing in the public forum, that is called “defamation of character” and it’s actually against the law.
No, you shouldn’t sue them, but it just tells you how serious defamation is. Talk to your parents first and let them help you decide how to handle it. You may need to get a teacher or your school principal involved, but something should be done about it, because it clearly seems to have gotten out of hand.