I hate my sister and I need help? No mean comments allowed though!?

My little sister is a pain in the rear! I hate her, she is disgusting and she always tries to be nice. Like today she was like, can I hold your hamster and I was like no and she cried to my mom and she came up there and took the cage to my sisters room. I just now got it back. Every time I am like studying for school or something she will come in my room and just annoy me. Today she tripped me down the stairs and I hurt my knee really bad. My mom was like what happened and I was like she tripped my and my mom sent me to my room while her and my sister went to get fro-yo and to see a movie. She acts like she is cool and has anger issues (she threw a remote at my head cause I was on a homework call) and she thinks she is going to "experience" things wayyy before me (she's 9, I am 13) like puberty. I always get in trouble because of her. Like now I got in trouble for saying move when I had to be somewhere. Please help me!