I think the only way to overcome an embarrassing past is to forget about it or at least chalk it up to being a person you would not normally be...hence being a drunk. You have an embarrassing past b/c you were drunk doing things you most likely would not do if you were sober. You just have to forgive yourself for your actions. Most likely you had no control of yourself/behavior anyway. Try to make peace with your former life.
As for seeing people from your past that were part of embarrassing moments while you were drunk...These people have probably been there themselves one time or another. If they can't forget it or forgive you then there is no need to feel bad about things. And you probably should not be hanging around these people anyways.
I have been trying to drop a lot of people from my past. Then I try to move on and not think about my drunken moments.