I've not had that strong of a desire to drink either. Have you discussed this with your physician or therapist that described the meds you are currently taking? Sounds like something might be not exactly right, but i would ask first.
Have you considered making a written plan to take a different course of action when you feel this way? Even though the cravings might seem like you nave no control over them, you still do. You are making a whole host of conscious choices along the way - get in the car, get money, go to the store, buy alcohol, drink alcohol...and so on. What about having a phone number of someone to call and talk about the craving while you are experiencing it? You could put it in your phone as an emergency contact for yourself. Or maybe come here? Tell us right in the moment how you are feeling.