I am a proponent of liver cleansings and fasting (I am planning a green tea detox very soon) but in your case I think it is a bad idea. You really don't know what kind of damage you have done to your liver and you are also detoxing from booze which can be dangerous by itself.
Also fasting/detoxing can be stressful not only physiologically but also psychologically.
Going on a fast or cleanse could make things even worst.
See your doctor first. If everything is ok, then once you have a couple of months sober under your belt, give it a go.