Before I broke off contact with my parents, I gave up arguing with them 'cause it seemed we'd go round and round in circles of "but you haven't lived", "you're too young", "it's just a phase", "you're too girly to be a dyke" and every other gay cliche under the sun. It's a waste of energy worrying over whether or not your parents believe you. It's your life, your feelings, your identity.
Acceptance, understanding and support are all different things and you gotta think carefully about what they all mean and which of them means the most to you.
If you seriously want her to know you're for real, take her to a PFLAG meeting or have a family session with a gay-friendly counsellor or summin.
Otherwise, I wouldn't worry about it dude.