I am sure your girlfriend is affraid that you will drink again and treat her badly again and this is something that it will take time to heal.
I quit drinking when my wife said quit or get out and I am sure at first she did not think that I would follow through with my promise.
Time sober will make her faith in you stronger and if this is what you want I can tell you that it is worth the effort.
As we face more and more things sober we become stronger and the desire to drink to handle our daily burdens diminishes until we embrace these trials as just a part of life.
Don't give in now. Your desire not to drink will become stronger than the need to drink sooner than you expect.
Good luck.