Hi! I'm new too but I think I might be able to help you...
I have a mum that is a LITTLE bit similar to yours. By this I mean that when I was 15 we had many, many arguments (I'm a girl, so... screaming matches) that always ended in me trying to apologise and my mum refusing to believe that I was genuine... sound familiar?
At 15, there's only really a few options out there for you. I definitely wouldn't recommend you try moving out- I tried at 16 and my entire family, including extended relatives, condemned me for it, plus it's about 50 times harder than you imagine, even with all the research. Looking back, it was a BAD idea. Unless you feel like your life is in danger, don't move out.
The best option is... grovel. Throw away that teenage pride. This is your mother, and at 18 you never have to see her again, but for now you must try to make this house as peaceful as possible. Buy flowers, write letters (handwritten, not emails), agree with whatever she says, DON'T talk to that girl (she's not doing you any good anyway), give her no reason to throw a fork at you and suddenly you'll find that life is easier. Trust me.
I recently made the startling discovery that my mother is the only person able to make me angry within 15 seconds when she is over 15000 miles away! Some relationships are like that. But after questioning, like you, whether or not I love my mother, I can now say that I most definitely do. So stick it out, because it gets better.
me whenever you like
EDIT: You'll find many of the guys posts in the relationship forums... I wonder why