Well, the thing is, did you hit her or she hit you?
If she hit you, then it's her fault, doesn't matter if you cut in front of her because even though you might have drove badly, she should have braked when you cut in.
But if you hit her because you didn't see her, then it's your fault.
I know you said she hit you, but sometimes when you hit something, it feels like the opposite. Anyways, you should tell the insurance company that she hit you, if you believe that's what happened.