She was considering telling me she couldn't see me anymore because of it already
Was it because of the drinking, or because of missing appointments? I just can't imagine a therapist who would give up on a patient - it doesn't seem right to me. (It's OK if she doesn't feel competent to deal with addiction, but she should have recommended someone). Just my opinion.
But yeah, you'll feel so much better being honest about your slip. Don't feel bad about it, though. We get used to lying when we're drinking or using....it almost becomes a habit. Sounds like you're doing all the right things, backbeat. Keep up the good work!