Who cares if someone knows you're trying to better your life? Sobriety is a wonderful thing. When I'm hiding my sobriety, it means I am setting myself up to drink again.
Now that doesn't mean I shout "I'm not drinking" to every single person I meet, but I have told my close friends and family. But I wouldn't care if they told others for whatever reason though I don't know why they would as, shocking as this news was to me, most people could care less about whether I'm drinking or not. My drinking and/or sobriety is of no interest to them.
I can't imagine going through life having no trust in anyone else. Seems like a miserable way to live.