Sorry to hear about your breakup - on a side note please breakup your message as it's basically a wall of text and some people may avoid it.
Anyway - the painful truth is that you will have to accept that she just isn't in the same place as you are. It's a difficult thing to do but it has to be done otherwise you'll present yourself as some needed little person who can't survive on their own if you start trying to push your way back into her life.
You will see a recurring piece of advice on this forum regarding breakups and it's a solid piece of advice; no contact. Cut your ties with her and remove the stuff she gave you - out of site out of mind. Kudos for being strong on the outside during the breakup, most people aren't.
I can relate really well with your situation; Im about your age and my GF broke up with me in September, a couple of weeks before I progressed into final year and we had been seeing each other for nearly 4 years! Let me tell you from experience that you need to embrace the feelings your having: cry if you have to, write down your feelings ( this is a good one! ), exercise a lot - basically do whatever it takes to vent the feelings that you have inside. The most constructive method for you would be to concentrate all your effort on your school work.
On a major note - stop the drinking. It's merely covering up the feelings that you have and these feelings won't disappear with excessive drinking. They can get worse, a lot worse. You could end up in hospital from half an hour of drinking like me - 2 drips in my arm whilst Im talking crap about her - you don't want to be in that situation! Also, you could come to rely on drink when something negative happens again so don't start now.
This new girl you have been seeing; don't go out with her. She will end up being the rebound for you and will only get hurt because of your lack of courage to deal with your emotions. Just explain your not in a place to start dating yet.
she said she cares about me a lot when we broke up but she has shown no signs of it. To me i feel like i dont exist to her anymore
Of course she hasn't shown signs of it - she broke up with you - can you really expect a person to display signs of love when she has just broke your heart? Essentially she is trying to remove you from her life because, and understand this please, it's easier on her. Can you imagine breaking up with someone only to have to run into them everyday or text them. The fact that you guys live 1200 miles apart is now a good thing - appreciate that.
Finally you are only 21 - you have a hell a lot of life to live and with that comes new women. I don't mean this in a derogatory manner towards women but have some fun before getting into a serious relationship - just don't act like a dick.
To sum up: vent your feelings, stop the drinking, concentrate on uni, implement no contact, work on bettering yourself.
P.S. Read this, 5 Stages of Grief
, applies to people going through a breakup.