Realizing I Can Never Have A Relationship With My Sister.

My sister is exactly 4 years apart from me. I am the younger, and growing up it was just the two of us. She is currently 23, and I am 19. I cant remember every being able to simply do the things I see my friends do with their sisters; hanging out, doing hair, make up, etc....When I think about my child hood memory with her, I can remember myself always begging her to play with me, but always getting rejected. Or just simply the physical fights. Its as if she hated me from the moment I was born. When I was really young, I would wanna be just like her. I would want to eat what shes eating, want to dress how she dresses. I would tell her secrets to try to get close to her, but in the end would be betrayed with her telling my parents every time we fought. However, my sister and i are just so different. I am an out going type that gets excited to dress up and go out with girl friends, while my sister is a more stay at home and watch tv. But I know that cant be the reason why we dont get along. She may hate me due to my parents giving me attention for my eating disorder I had experienced in high school. During my high school years, I became anorexic and soon became bullimic. It took me 3 years to fully recover, and have bits and pieces of my memories missing for these 3 years. I do not remember my sister being in my life for these 3 years at all. I just remember my parents not knowing what to do. During these times, I can explain how sorry I am to my family. Getting all the attention from my parents and creating so much pain. I know my sister hates me for this, and I just cant be anymore sorry to her. My dads side of the family cut me off of the family due to this (which i know is wrong), and thus I am unable to attend any of the family dinners. My sister is liked from both of my mother and fathers side, since she acts like the perfect child. And she is. She never really broken rules, and obeyed my parents at all time. I was the one who would go out and stay out till late with friends. She would always make fun of me use me as jokes to her friends on how crazy I am..Most of it which isnt true..But i just laugh along with it to satisfy my sister. The only thing I was is a relationship with her. But I realized that wasnt going to happen. She has been telling my fathers side of the family untrue stories about me stealing, and that they should be careful with their stuff when Im around. And recently found out she told my best friend I had an eating disorder..something i still want to be a secret or atleast wanted to tell her from myself. She had also specifically told me she does not want me in her life, and wants nothing to do with me. I always thought "Blood is thicker than water", that since shes my sister no matter what, she would love me. But i was wrong. I do not know why she has so much hatred towards me, and for my whole life just wanted to be her friend.