I think you know that there is no easy answer as to how to stop drinking. I firmly believe that it's the motivation you have behind you, rather than a particular program or method. I hope that you shift your thinking from feeling helpless to taking control. You are the only one who can change yourself.
I also think it is important to understand and know why you began drinking on Sunday night. It's only by understanding yourself and your motives that you can learn to make changes in your life. I was a closet drinker as well, and I totally understand the abundance of shame that goes along with hiding the drinking from people.