I can't emphasis enough on what others have said about giving her time and space. She does need to work this out on her own and maybe go to Al-anon. You need to focus on your sobriety and not being deceptive anymore.
I lost a girlfriend over lying about my drinking. I made up stupid lies in order to protect my drinking. She didn't like me drinking, but she hated the lies I would tell in order to drink. It eroded trust in our relationship.
When I got sober, I apologized to her (once again), but she remained skeptical. I became frustrated that she wouldn't instantaneous trust me again. As the self-seeking, instant gratification person that I was, I demanded her to forgive me and trust me on the spot.
It was the worst thing I could have done. It exacerbated our problems and we eventually broke-up