My sister betrayed me?

[Cass]

First off, wrong section.
Second, your sister is making up lies about you, slandering you, and making you look bad in front of others.
I don't know why, but I do know one thing: there is no relationship to patch up.
All you can do is move on with your life.
Find your own way, study hard, get a job (or focus on your current job) and talk to your sister like you would talk to an acquaintance.
If your parents ask what's going on, tell them to ask your sister since she's the one making you look bad.

Good luck.