I am the spouse of a recovering sex addict. Your gf will never truly understand your addiction. That was the first thing i had to accept after discovery. Addiction of any type is the definition of insane. I am in no way am saying that addicts are insane. The addiction itself is insane. Doing the same thing over and over expecting a different result. Someone that has never experienced that addictive cycle will never really be able to understand the cycle. And thats okay. Your gf needs just as much support as you at this time. Relational betrayal is the hardest thing to recover from and she is likely even experiencing severe trauma. All you can do is support her, be gentle and fully honest, at the same time doing everything and anything to stay sober and be in recovery. She would highly benefit from some outside help, therapy, life coach that has experience with trauma. It is very important for her to talk to other spouses of sex addicts so she doesnt feel alone.
Showing her how serious you are about recovery is key to regain the trust. So if you are still acting out how can she begin to heal as well? I discovered my husbands addiction in 2011, he was sober for 18months and i was miserable. After that 18 months he relapsed, and i drew some very concrete boundaries and consequences. He then finally gave me FULL disclosure, therapy, polys, inpatient rehab, attended SAA, marriage therapy. That was 4 years ago . He is still in recovery , sober and has never slipped or had relapses in the whole 4 years. Our marriage is better then ever. I still deal with triggers and trauma daily, but we are doing okay. There is hope!!!!

I am also a spouse of an addict and agree with candycin that the best thing you can do is show her how serious you are about recovery. She's going to need a lot of reassurance and comfort and even then there will still be dark days.