I'm not sure if my advice will help- after all, I have a lot of experience at being drunk and just a little at being sober!:rotfxko But I agree with the previous posters, better to fess up and be honest. I also agree if that if that person is hanging threats over your head you may want to consider a referral for another therapist.
Don't beat yourself up no matter what. Sure you had a slip but no one said it would be easy. Most hardcore alcoholics can't kick it cold turkey on the first try. Just hang in there and do your honest best. That's why they say one day at a time.