Like Cherry above, I can't comment on your exact problem but I can tell you what happened for me.
I decided a few years ago to stop eating junk, stop eating packaged and processed foods, and avoid fillers and chemicals and preservatives. It doesn't mean I never eat any of that stuff, but I've cut it down to less than 10% of my overall diet. I concentrate on eating lean meat, veggies and fruits, and whole grains. I try to get at least 25% of my diet from healthy fats (olive oil, peanuts, almonds, avocado, etc.)
In the last couple of years my skin and hair have gotten less oily. I don't break out as often. My rosacea on my cheeks and nose has faded somewhat. My fingernails are MUCH healthier and don't crack and split the way they used to. My hair is thicker and less likely to break and split.
Aside from those external things, I used to go to bed every night with horrible heartburn - sometimes waking up in the night with reflux that would make me cough and gag. I used to buy Rolaids by the case at Sam's Club. Now, I haven't had heartburn in over a year. I honestly can't remember the last time.
I also can tell a real difference in how I feel when I *don't* eat healthy foods now. Used to be I felt bad enough all the time that I couldn't tell when something I ate affected me. I used to wonder at the people who would say "oh I can tell I ate too much salt food ysterday" or "wow that dessert was too rich" (I mean seriously whoever heard of TOO rich, right?). Now I'm one of those people. I can wake up in the morning and tell when my sodium the day before was too high. I can tell from the way I feel that I've been slacking on my nutrition. If something is too rich or too fatty, I can taste it and feel it weighing down my stomach.
It's amazing the way your body will tell you when you're doing something wrong - if you just give it the chance.
So I'd suspect that even if your eczema doesn't completely go away, it will become much better with healthy eating.