She sounds immature and bratty, but you don't sound like the best friend either, to be honest. I know what it's like to have loads of work, but you have to make time for other things. Saying you can't afford two hours out of an entire week is a downright lie. If it's true, I'd be very worried and reconsidering whether I was on the right course. It's not normal to work 24/7, no not even at Oxbridge. When I'm home for holidays my old friends call me and I still feel I should see them if I want to continue the friendship, even if I'm really busy or can't be bothered to go out. It isn't that much to ask. I find if I go out with them one night, or even just to the cinema or for lunch if I'm really busy, they stop nagging me about neglecting them. You should ask yourself if you really want to be friends with this girl because if you did, I think you could spare 2 hours for her.