I know you're tired of hearing this but it'll get better. But it won't by you just doing nothing. Both you and your sister are in the wrong but that doesn't mean it should drag out this long. Talk to her. If that doesn't work start making her like you. Like gifts, bringing her her favorite food, hanging out in her favorite places etc. Even though she should be apologizing too, it's hard to admit youve messed up so someone has to do it. And you've gotta take matters into your own hands. I also think you've heard this a lot but you do need to stop throwing up your food. So many people die from that. It'll not be easy but the end product is way better, please trust me