If there’s one thing I’ve learned about this diet, it’s that everyone has different symptom triggers, and they can be really random (and thus hard to pin down). I also have eczema as my main symptom, and in my case, a serving or two of nuts, beef, pork, millet, or milk-based kefir (all of which have triggered symptoms in other people) will not cause my eczema to noticeably flare up. However, I’ve found that eating eggs (even once) that are not 100% organic and hormone-free will cause my skin to worsen and stall my progress by at least a week.
Since you’ve suddenly added a whole lot of foods at once, plus anti-fungals, it’s hard to tell what triggered your symptoms. I second what Abel recommended re: the anti-fungals (i.e not to take them, especially if eczema is your primary/only candida symptom). I also should mention that I agree with Javizy’s mention of oils as being good for eczema, but I’d add fish and olive oils to his list.
As far as finding the culprit, I would immediately switch to organic produce and at least hormone/antibiotic-free meats and eggs. I would also lay off the kefir for the moment (I don’t know if you used new grains or not, but if so, did you remember to discard the first two batches?)
My experience is that die-off symptoms are inversely proportional to eczema healing. In other words, as my eczema healed, my other die-off symptoms (headache, dizziness, flu-like feeling, brain fog, constipation, etc.) got worse. Whenever my eczema would flare up, it was a sign that I did something wrong, not that I was progressing. Your case could be different, of course.
(Also, if you haven’t already, I’d recommend reading this thread, as it also deals with candida + eczema: http://www.thecandidadiet.com/forum/yaf_postst1949_Eczema–candida.aspx )