Oh I know the answer to this one...it's "head held high" of course. I had been through Hell and came out the other side. I honestly gave two fat rat's asses about the gossip mill. Let them talk. You get on with the business of living!
I just focused on my work and did not discuss anything personal except with a trusted few. You've made a giant positive change in your life by quitting drinking. What you've done is something to feel proud of, never ashamed of.