I like what DC has said. Keeping it a secret means that you have an opportunity to consume if you so choose and no one would know the difference. That being said, your decision to quit and keep it a secret is completely up to you.
I dont talk of my recovery with people. It is not a part of the conversation. I am very open about my life and if it were to come up in conversation, I would not mince my words or hide the fact. The truth is available to anyone who questions but I am not on the rooftop with a megaphone letting the world know that I am an alcoholic. They probably already know anyway.
Stay close. Do what makes you feel comfortable. No one can tell you how to live your life. If you can find one person for face to face it would be helpful though.