You think I'm annoyed that she keeps texting every day but doesn't reply?

There are actually two reasons for this situation. First, she may not have received your letter, and second, she thinks you are really annoying. But now you are not sure what the answer is, so what you have to do now is to determine what the real reason is. If you don't get it, tell her clearly that you care about her. If she thinks you're annoying, tell yourself it's better to give up.