How can I get my fifteen year old sister to believe me?

Alright, so some family members told my sister that I chose my aunt to live with over her because I hated her and that I was lying to her and all this other crap. I've been trying to tell her I'm living with our aunt because I have no other place to go and I needed to finish school here first while she lives in a whole nother state. Our conversation ended with, "I don't care, you chose your family" is what she said to me. She's just a year younger than me and the only person with legal guardianship of me is our aunt considering both my parents had ped away while her dad is still alive. The rest of our family is starting crap between me and my sister and the last thing i want is for her to hate me because family is starting drama and all that. All i want is to try to get her to believe me. I hate that I can't do much about this unless I was face-to-face with her.