A few days ago, I sent this girl a letter over Facebook (lame) saying that I really like her and would like to get to know her. She didn't respond. When I talked to her the next day, I said I was sorry I sent it and didn't mean to come off as a creeper. She said she wasn't sure how to respond to my letter, so she didn't write me back. I could tell she was shy, but I couldn't tell if she thought I was annoying/creeping. I talked to her the next day and she seemed to be happy to see me, but I wasn't sure. I really want to talk to her, but I don't know if she wants to talk to me. Am I annoying? Should I back off? In the comments, can you tell me how I could approach this situation?

What you really need to do is ... relax about it.
Let her get to know you. It won't be the end of the world if you can't have her. But if you relax about it and just let her get to know you... you might end up with a friend who likes you. Maybe even more if it works.
But you can't rush things. Rushing things just leads to uncomfortableness and being awkward and then worrying that you're doing too much or too little and then you over-compensate for what you think you might be doing wrong. and pretty much you think it to death.
So be polite to her and friendly. and see if she responds to it.
Gotta be in it to win it and if you lose, such is life.
I'm sure everything will work out, I mean, if she seemed happy to see you, then she can't be annoyed!
Good luck, I hope things go how you want them to!(:
I think people sometimes play games because they're afraid to be honest (this isn't you, by the way), and sometimes people play games because they're afraid to deal with honesty (this might be her). Either way, honesty gets replaced with games that nobody really wins. And what is the point of a game if nobody wins? That's worse than a game!
Stick with the honesty. Maybe just release it in small doses and see what comes back.
P.S. If the definition of "creeper" is someone who was honest, someone has got the definition wrong.
From personal experience, they like to imagine you've come to a (very) slow realisation that she's the most wonderful woman who ever existed (even if you already knew that from the moment you met her and she took your breath away).
Honesty is wonderful in a long-term relationship, but to get that relationship sometimes you have to pretend to be less interested than you are. I know it seems odd to us men, but we seem odd to them too. I imagine there's all kinds of things they do to smooth the waters with us.
I hate saying this because it sounds like a game. Maybe a better way of looking at it is patience. Make the smallest possible indication that you're interested, even if it seems too small to notice. Just a second of eye contact, that kind of thing. If you've gone too small, be slightly bolder. There's no such thing as too small, though. Too little and she won't notice (so you can try again). Too much and you get a negative reaction that's difficult to recover from.
I wish it was as simple as noticing a girl, liking her, and just telling her the things you like about her. In the long-term, it is that simple and you can be honest (thank God). It just doesn't seem to work that way at first.