Welcome back!
Please find a recovery program that works for you and work it. This cycle can STOP , it starts when you start working a program.
Get a good support system behind you. Sounds like your GF may be over all the promises, that is understandable, a persona can only take so many "i'm sorry, I'll stop" when in fact the best thing you can do is SHOW her and yourself, you are worth it, and to do that you remain sober and work on you.
I totally understand how you think you have a sex addiction. While I was on meth or booze, I was so slutty (honest program worker here). I am disgusted with what I did while using, however, I know that is not ME, sober me.
Now that I am sober, I found out WHY I was that way, what lead me to do those things.. Rude awakening of how much self-hatred I had for myself and lack of attention from... anyone...
Now that I am clean, my self-respect is in tack, my infidelities are no longer existent.
Daily amends for me are remaining sober, this way I am gaining the trust back from people and trusting myself.
I wish you the best. DO you, and get better!