Save yourself. Really. Good on you for recognizing your strength, and making a great start to your life, your family will always be there, but you got this chance to be independent of their stress on you.
You're more fortunate than I to actually be ready to be moving out in a few months...I would definitely establish a good distance between you and your parents if they treat you like this.
You sound like the kind of daughter parents should cherish. I'm sorry your parents don't support you as they should. Move out when you can & make your own life, but don't burn your bridges.
You will have 1000's of people pass through your life, but only one family. Love & respect them, and never give them up!
if they never supported you then yea , you should cut contact or at least i would : /