oil of oregano is the nature's strongest anti- parasite anti-fungal anti-bacterial agent. Consider buying a high quality oil of oregano and try rubbing it on your skin. You can also take oil of oregano internally in limited amounts (a few drops at a time).
A high quality oil of oregano is produced by North American Herb & Spice (NAHS). You can find this in health food stores like Whole Foods. I found a website on the web that sells this at a lower price than my local health food stores. Here it is: http://www.vitacost.com/NorthAmericanHerbSpiceNAHS
I have eczema and I personally use the Super Strength formula by NAHS on my skin when my eczema gets worse, and have seen that it cleared many areas on my skin. The burning, the itching and the inflammation are definitely gone when I use oil of oregano.
You can also do your own search on the web for a high quality oil of oregano. The reason that I suggested NAHS to you is that it is the first company to start producing oil of oregano in the USA using high quality oregano.. And their oils are used by many researchers to test the properties of oil of oregano.