I have similar anxiety about attending therapy because yes, it's very scary to open up about our emotions. But you are doing the right thing by attending your sessions. It is natural to want to push away the thoughts that make us feel shame (I am guilty of this too).

My best advice would be to treat yourself to something nice after your session. Rather than trying to drink away the anxiety, you can just keep your little reward to yourself in the back of your mind. Maybe that can be a different way of motivating yourself to get your foot in the door to your therapist's office.