The misunderstood villainess is in love with the villain

I reincarnated I didn't see a white light. I didn't regain my memories due to an accident. I wasn't reborn into a world of magic. In this life, I have to deal with my brothers and my baby sister, who follows me like a lost pup. After a few years, I could finally go to a school for nobles. Every day I would work hard and have been at the top of my classes, but because I caught the interest of the prince, one of the other students uses me as a way to get the prince's attention. She makes me appear as a bully, always taking advantage of me being alone. So everyone thinks I'm a terrible person, even my twin brother thinks that I did all those bad things. Though in all honesty, I don't like the prince, I find him annoying clingy and possessive. I'm not his property, but he treats me like a possession. The person I like, though, has no idea I like him, and he loves the girl who keeps pretending I'm bulling her. Though he is also possessive, he isn't as annoying as the prince. The only thing is people keep calling him a villain because he has killed people before. Please look at me. I'm not a terrible person; I just keep being framed.