I would transfer your app to oxford and see what happens.... I'm sure your parents would want you to go to your best choice school, but if it's a question of you being truly needed at home, or a dire medical circumstance that is threatening life, then staying in GA might be the best bet. I think you should tell you parents how important it is that you want to help out, and THEN ask what they think. Tell them how you feel about the schools, and let them help you decide.
An internet forum really isn't the place for this decision. Talk to your parents and really be honest. Go with your gut on this one, not what I, or anyone else, say.