What are you going to do about the physical withdrawal? What medical and addiction-recovery- specific supports will you have to protect against going back to the alcohol self-medicating / relapse loop?
The relapsing is happening because you have created a physical problem. CBT is a psychological tool, not a physical tool. You need a physical, medical tool, and you need it to be more directly, specifically related to addiction recovery. (Also, you’ve tried CBT before, as you share here, and you continued relapsing. The solution you’re looking for is probably not CBT; if it were, it would have worked already.)