Your mum loves you more than anyone else in the world, I'd be willing to bet on it. Things can get very diificult at times- remember you are in a major period of transition right now, between adolescence and adulthood, and this is a tough and stressful time in ways you may not realize right now. It's got to be affecting your mum too.
Make it up with your mum. You know how to do this better than anyone else.
Even if you don't end up staying in your house, both of you will feel massively better and both of you deserve to feel massively better.
Take some time over this. if it helps, have a friend or relation sit in when you talk to your mum. This person should not intervene, and should ideally be very fond of both of you. It may help to keep things calm. Maybe this won't work for you, but it's just a suggestion.
Whatever your argument was about, the issues are real, but they can also be worked out. Remember the bottom line, that you love each other very much and want the best for each other.
I had a massive argument with my mum too, three nights ago. Sometimes this takes lot of work, but you will be OK and you will work things out. Don't worry too much about the details- where will you live, etc., because if you sort out your relationship, most of the details will fall into place.
Good luck, I know how you are feeling.