Try to remember not to judge others too quickly.
It could just be that they have one of those faces that always looks like they're disinterested/angry/whatever. She may not actually despise you. That competitive vibe you're getting may be entirely in your imagination. After all, she's pretty cool on paper. She's still adjusting, right?
Sorry for the cryptic post. I'm a little paranoid about developing female friendships and blogging. They are as bad a combo as soju and vodka/crans. So I hear secondhand... from her.