I am surprised no one replied to this one. I believe this is a common problem people face, trying to get over a relationship. First I want to say bravo to you for ending this one. When someone has a substance abuse or drinking problem they need to get sober first. Once they have committed to recovery than they are in a position to work on their relationship. If they are not willing to get sober than they will not want to work on improving a relationship. Nothing personal they just want to use, more than they want to love themselves and you.
Now getting over a relationship. Release yourself of any guilt and relax. Take the pressure off of yourself. It takes two committed people to make a relationship work. Otherwise one person is always rowing the boat with one oar. It could take a while before you are ready to get into another relationship. The longer the relationship the more time you need to recover from the fallout. Getting back on track for your life will be your priority. Learning to love again will happen one baby step at a time. Give yourself at least a year to readjust to life without the alcohol abuser. Get into a support group , or stay close with your supportive friends to help you get through this most difficult time. Being with groups of people will take the pressure off of dating until you are ready. An extra added benefit is you might meet someone more suitable amongst a group of friends. Know that we are all here to support you.