I'd take the safe route. You drink quite a lot and are already concerned about heavy withdrawal, which adds anxiety and fear to it. Do you have any condition that would make it dangerous for you to continue drinking until your appointment?
Me personally would wait until the appointment, to be safe. In the meantime, I'd focus on your motivation to quit. What you will do with your new life. The money you'll safe. Get mentally into it so that you're truly ready once the appointment comes.
That is what I would do, IF I couldn't contact my doctor at any time. I don't know what it's like where you live, but over here you can call a doctor for a phone consultation 24/7. If that is possible for you, do that. I promise you it will be a great help.