How old is she? It sounds as though she's in the high school years, in which case she (should) eventually outgrow that mindset.

When my sister and I were in school she was known by many other students as "Trebyn's sister", and it annoyed her a lot. People she didn't even know would go up to her and ask her if she was my sister, and then that would affect how they treated her. As an adult it still bugs her when someone asks her if she's my sister, but that's a rare occurrence now. Out of high school the world is totally different, and you don't get put into categories as much as the clique-ish high school environment. You get to define yourself through your own actions.

Ultimately that's probably what your sister is really mad about. That her identity is not yet her own. That's just the reality of that age though, and it's not your fault at all. You're the target of her blame, but if not you she'd blame parents, friends, wealth, her appearance, the family car, etc. It's her trying to define who she is to the world, but it's unfortunate that you're taking the brunt of her frustrations

One of my own friends was embarrassed by her brother and used to tell people that he was her half brother, even though they were actually fraternal twins. They wound up becoming really close in their upper teens, and she felt really bad for how she treated him.

People have to learn to accept themselves before they become willing to accept others for who they are. It sounds like you have a better idea of who you are than your sister does about herself.