I don't think you have an issue. We're humans after all, and it hurts when we're rejected. And frankly I didn't expect her to confirm that she was distant. Girls (and people in general) are usually like that. We become defensive and deny that we are avoiding somebody...
>"...and not asking her out from desperation."
This could actually sent a different message -- that you did ask her out out of desperation... When you have to say something like this even if its true (as it is), it never sounds good. So, if you left that out and just told her: well I liked you but I don't want that to ruin our friendship... It's all minor things and people shouldn't over-think but they do.. So you have to live with that.
It's probably good to just let it cool off. I'm sorry but it sounds that she wants to take you off her back. And there's a way to check. Maybe give her some time and space, and if she doesn't call you anymore, then you knew it from the beginning...
If it doesn't work out, then it's time for you to move on. You've actually got very good things out of this.. changed your appearance for the better, looking for better job...
Keep your head up!