for what it's worth, I had some skin issues before fasting. Not as bad as yours, but dry skin and dandruff. That kind of stuff.
It cleared up after my first week long water fast. And the skin gets even better after each fast. I have one weird little scaly spot on one finger that keeps fighting me, but other than that, I've gotten lots of compliments on my complexion and my spouse keeps commenting on how smooth my skin now is.
It looks like you would need more fasting than 1 week to resolve your issues, but if I was in your condition there would be NO hesitation. You could try a long fast or several shorter ones. For instance, 1 week a month for the next several months.
True fasting is dry fasting. Water has stuff in it, minerals and such, but Water Fasting is the safest and most effective form of fasting for most people.