Speaking as a mom of a 14 yo daughter, it sounds to me as if your mom is really hurt and angry right now. Let her cool off and then try again to apologize. I always thought once I was a parent I would be able to set aside my personal feelings and instead just focus on my children, what they were saying to me and what they needed. Well, I try to do that but you know, moms love their kids more than anything. And even thought we’re older and supposedly more mature, since we love our kids so much they are also able to hurt us in an equal amount. So sometimes we’re hurt and angry and we say things we don’t mean. I expect you and your mom will make up and she will forgive you, because you are her child.
Oh, and like was said before, your mom’s anger cannot affect your relationship with God. If you confess and are sorry for your part in the argument, He will forgive you.