Hi Isaac,
Accepting that you have a drink problem is the first step on the road to dealing with it ~ so well done. Actively addressing it is another good step, but you probably need help and support, if you haven't organised some already ~ something like Alcoholics Anonymous.
It's good that your future looks bright so really do try to keep it that way.
Now get some help and work at staying sober and sorting out this problem. Stay honest with yourself and others over this.
Consider why you drink & what makes you drink to excess. Then try to find alternative ways of responding to whatever triggers your need for alcohol.
If you still love your ex, and she broke up with you over drink-related issues, I think that it would be worth writing to her and telling her what you have told us. Good luck!