I am sorry to hear this, but as you said, it is a part of detox. When I fast, I get rashes too, except for last few fasts. Acne I have never had, I have fasted since I was seven.
There is no way of telling how long will it take to get rid of it he acne. You really have to try a few days more and then go on a juice fast.
Also know that fasting with water is not starvation, starvation actually comes from eating partial and junk foods.