Been there, done that. The shame was really bad for a while - I was ashamed way before I quit drinking, and I drank to make the shame go away - of course that just led to more shame. I did a pretty good job of beating myself up for a while after I quit, and a couple of other people got their punches in, too. It was pretty bad. BUT - I knew I couldn't change the past. All I could do was stay sober, show myself and the world that the drunk me was not the real me, and keep on going. Now, over 2.5 years sober, I can hold my head high again. Most people forgot about my stupid behavior. And if they didn't forget, they know I don't do that stuff anymore and see me in a different light.
That's a long-winded way of saying - time heals. Stay sober, apologize to people if you actually hurt them while drinking, and start learning to forgive yourself. It's not going to happen overnight. But it will happen.