I have occasional flare ups with eczema, mostly because I eat and drink too much of stuff I shouldn't and because of the weather (usually really hot or cold). I have found for me that the one thing that really helps me calm these breakouts down is 10% sulfur soap and sulfur ointment, both of which can be found on the internet. As you could imagine it smells a little bit, but I've never had anybody say anything to me about it and my wife says she can only smell it if she gets really close to me.
I don't know if you should use it if you ever get to the open sore phase, but ever since I started using it when I noticed the beginning of break outs I've never got to the open sore phase again. I also use ACV, coconut oil, and turmeric and that seems to help as well. Hope this info helps. I thought I should post about it since I didn't see it as one of the many potential remedies.
-Eczema sufferer since 2012