Why are you with someone like this? It sounds like a strange question, but it isn't. Anxiety, depression, excessive drinking...2 of these are very serious emotional or mental problems that she may never get past. Anxiety is a lot more controversial, since it seems so many play that card just to avoid doing something they don't want to do.
Anyway, it's not surprising you're getting annoyed. What you need to realize is that, as your relationship deepens, the stakes get higher. This will worsen until you finally give up. Also, on that secret drinking, this isn't "normal" behavior. What I mean is, if she can fool someone for a week, she's capable of fooling her parents and even you. I'm a substance abuse counselor, and this is a very common pattern. Secret drinking is always a big red flag.
Honestly, even though I doubt you'll do this, I think you're best off telling her you love her blah blah, but right now, she's got a lot of things on her plate she needs to work on, but you're just getting in her way. This has the additional benefit of being true. As long as she can fixate on you, she feels more free to ignore this other stuff. She won't be the only one who pays for that. You will, too.