How do i show my gf she can trust me...........plzzzz answer fasttt!!!!!!!!!!!!!?

ok so i goto this school hhs and she goes to this scholl ehs their highschools....but we live in the same neighborhood sienna and i see her everyday =] =]... well lately iv been actin wierd with her cuz she been changin and yea i dont like it so everyonce in a while il catch a attitude which i really dont mean =[ =[ =[ look i love her sooo much , anyways well my past isnt to great either, i used to just go mess around with a hole bunch of girls because i never trusted any and i didn want to get hurt... well their been times where girls from my school will call her phone and claim that iv cheated on her, their been times that someone hacked my myspace and put some dumb messages between me and another girl, and then their been times when just a random girl will call and claim that she made out with me b4 we went out.... so yea its hard and its happen so many times that she doesn trust me cuz she belives everything everyone else says. so it just happened again and her ex best freind told her that i cheat no her at my school so of course se belived it and we fought and fought . so after arguing i broke up with her and didnt think, so yea im stupid i kno... but then my freind came over and he allergic to cats so we went to walk around well he took off runnin to some party and i didn want to go so i stayed out side and yea well it turned out it was this girls name taylor party and my gf dont like her. well someone called her and told her i was inside the hous and **** so yea, but i wasnt i was outside waiting for my freind so we can leave, he just went in for food then we left, well i called her phone a billion times b4 she answered and i talked to hershe said that she talked to this girl name tetra and that she said i poke her in the stomach and flirt with her when i dont =even really know his girl and yea i wouldn do that, well i talked to her this morning and im pretty sure were goin to get back together but how do i show her that all this talk bout me at this school is fake and not true plzzz some one help