Should i get out of this relationship?

I am about to turn 16 and there's this girl who ive been dating for a few weeks who is 17 about to turn 18. We have a LD relationship because she lives 430 miles away. Right now i am lost and confused because i don't trust her and she is a little childish who am i kidding she is very childish. ive known her for about 3 months now and we got together this month. she told me herself that a LD relationship can survive on trust and communication, but we don't communicate as well as i want us too she is always quiet on the phone to the point where she goes to sleep (man i hate that) and we dont talk about nothing. She dont trust me and i dont trust her. lately she has been acting childish accusing me of cheating and hanging up on me when we are discussing a problem. i told her about one of my exes who i am still in love with and she got jealous and i told my ex about what she do and she told me every relationship has problems and to stay with her... as bad as i want to break up with her i love her and i want to try to make this work and she swears she loves me too but it just mite be a game. i dont know what to do because the childish games are expected from someone my age not hers