The way to help her is not trying to change her mind. Show acceptance. You love her, but the way you manifest it hurts her.
You have to learn how to love. I don't mean care for her. I mean love, as in taking her in all: the good, the bad, the ugly.
She's allowed to be stubborn, sad, angry, suspicious. Do not admonish her for showing those "bad" emotions, specially if you don't think they're warranted. All you can do then is ask how she feels and whether she'd like to get a hug, or perhaps just be left alone.
It's going to take time. Building trust always does. But she won't listen to you until you become a person she reaches out to when things get tough. Right now it sounds like she doesn't feel you got her back.
I sincerely hope for the both of you that you can deepen your relationship before you go live on your own. It really gets much much harder after that.