How can i prove ive changed?

Me and my girlfriend of 1 year and 8months just recently broke up. She has been my best friend since 6th grade during high school we both kinda did our own thing but always stayed close friends. the summer we graduated we started talking alot more and at the end of summer started going out. Everything was perfect everyone of our friends loved us together my family loves her and hers loved me and ive never had a girl love me so much and of course ive never felt this way about anyone. Recently things have just been getting in a rut. Ive been straying off my school path and nt focusing on what i really want and havent been treating our relationship with enough respect. About 3 weeks ago we had a little break up because of me. I was set on going to the miltary cause i felt i wasnt going anywhere and she wouldnt accept that so i broke up with her. Then we noth saw real quick niether of us wanted that. a week after we got back together and i promised her everything would get better my dad and me started having a fall out a bad one he was makin me feel really shitty about my life. I got real drunk off whiskey and when i came home me aand her began to argue and i took my frustration out on thegl tables my mom had just givin me. It was in her apt and it scared the **** out of her she called the police on me but i left as soon as it happened cause i instantly knew i ****** up. Its been a week since it happened and she says i better give her her space or ill push her away. Some of my friends who still talk to her say that they can tell she still loves me and misses me but she says she doesnt want to be with me ever again. I gave her flowers and letters at first but i have stopped now i heard she has kept both the flowers and letters. she also did not tell her mom what happened because she didnt want her to know i did that "just in case". im taking anger managment cles now and i have enrolled in school for the fall ive been trying to run all the time to replace my hurt. I want her back and i know she is the one i just hit rock bottom in front of her. She says she understands why i got so mad but she is still really scared. So does she still love me? Is there any coming back to a guy like me? How can i make her see i can make her happy again and that she will never hurt like that again