Apologize. This isn't always as obvious as you might think. You probably don't really hate your Mum. She does not want you to leave. She wants your respect and your words hurt her. Are you sorry you said that? Swallow your pride and tell her. At least try that first, before you do anything extreme and compromise your future.
any chance she will have moved on about it or that you could apologize when she comes home if you have no where to go?