Go after her or not? Does she just seem nice?

Okay, firstly. Do NOT send her love letters. Unless she 100% feels the same way, and you guys have a kind of relationship where that's okay (boyfriend and girlfriend, but from reading your description I think not), it will come off as creepy. Even if she doesn't think it's creepy, she'll probably tell her best friend, and that friend will think it's creepy. Notes are really cute, but a full love letter will be a little creepy.

That being said, you need to talk to her. Girls are confusing (we don't even know what we think sometimes) so there's no guarantee that she likes you. But if she does, she's hoping that you initiate contact. Just talk to her when you see her, keep the conversation flowing, stay interested. But don't be obsessive, or smothering. You need to keep a level of not-the-guy-that-is-obviously-head-over-heels-for-me. When she says hi to you, say hi back. Ask her what's up, how's her day going, does she have any fun plans for winter break, etc. Casual topics that make you seem interested, but not overly so. Stay open and nice, tell some jokes, loosen up, have fun talking to her.

I really hope I helped!

Dude, it's your choice. There are better girls out there if she isn't for you. i've experienced that a lot of times and let me tell you that i end up hurting myself. if she really is for you then go for it. don't rush her because relationships never last long if you do. try to aim to be her best friend so that she will be comfortable in talking to you. and whenever she has problems, comfort her and tel her that you are here for her.

First of all, is she single. If so, show her signs that you love her. Send her love letters, girls are so easy to catch when you send them love letters lol