Good for you for forcing yourself to eat. And good for you for at least telling your mom about the eating part-that's a step forward and will hopefully give you the courage to continue a communication with her regarding what's going on.

It almost sounds as though your friend is going through something of her own and is either crying out for attention, or trying to push you guys away from her...if things were okay, she probably wouldn't have gone through that whole thing with asking you and your other friend if you guys hated her. Then I guess because you didn't react as strongly as she would have liked-she made up the story about the guy that you have been talking to. She had to know it would hurt/upset you so...

I would try to talk to this friend a bit more and try to see what's going on.