How can I help my sister?

Hello everyone,

So, I have a 13-year-old twin sister, and she's not doing so well at the moment. I'd say we get along pretty well. We don't really argue (we used to), but we don't talk much these days, and we almost never do anything together.

She goes to a different school than me. She hates school and is bullied by two girls. She has a friend there, but they don't see each other very often. She doesn't see her friends very often in general.

She's a shy person. My parents are both good parents. My father always wants the best for her and would cut off his hand for her. My mother is always open and talks to her often.

Well, she's always had low self-confidence, but right now it's like she's depressed or something. She just stays in her room using her phone and has no interest in doing anything else. She barely eats and doesn't like very many things. She's often sad or in a bad mood. Today I went into her room, and she just started crying, and she wouldn't tell me what was wrong.

My mother has already made an appointment with a psychiatrist. I don't know. I used to annoy her sometimes as a child, or I'd put her down in arguments. She said she'd like to know more about my life, like who I'm into at the moment and things like that, but I don't like talking about myself or private things like that. Not with anyone, except maybe my friends. I sometimes worry that it might be my fault because I should be doing more with her or because I annoyed her back then, and I don't know what to do.