I did a 10 day honey and water fast. My eczema cleared up, not all at one time but slowly. I was in Thailand when I started the fast and by the time I ended in Japan, about 1 mth later, it had pretty much healed. I didn't need lotions, hardly thought about it, itching was gone, but still some dry skin. Still, to be free of worrying/thinking about it all the time was wonderful.
My fast was honey and water. Occasionally, I did drink some green tea. My advice is to try and stay busy, but don't over do it. I slept a lot and went out to people watch just so that I could have something different. Other than that, there's not much more to do. Just remember that if you do break down or whatever it's not the end of the world and you can pick yourself back up at any time. Oh yeah, and I didn't notice much from the fasting at first, but on maybe the 4th day, I started feeling more clear. I could smell things I hadn't smelled before. Everything was more clear.