Well, I have been in therapy for years and from my point of view it is not the therapists job to judge you on your drinking. Your therapist is there to help you with your problems. Alcohol has been a problem in your life and I am sure there are other problems and her job is to help you see the reasons as to why BLAH BLAH BLAH...... Get what i am saying? Judgement is not her job. Tell her the truth so that you can move on and get down to the real work. Holding this "Secret" in is stopping anything productive from happening. If she decides that she can no longer see you then you will have to find another therapist.
Has she stated that she will terminate therapy if you drink again?