Eczema is term that can be applied broadly to any kind of skin condition that results in flaky, irritated, itchy skin. Psoriasis has many of the same characteristics of this general condition, including cause (hereditary), symptoms (described above) and effective treatments (light therapy, for example).
The similarities between psoriasis and eczema inspired me to mention this new treatement that has been found to help people recover from severe eczema and/or psoriasis: Bleach baths. You might ask your doctor if he/she thinks this would be worth a try.
Promising results for this treatment have been reported through a variety of news outlets and online forums (including here and here for example).
The prescribed concentration for these bleach baths is between a 1/4 and 1/8 cup bleach for a full bath. This seems to kill any infection on the surface of the skin, thus allowing the body heal from the damaging effect of these skin conditions. Everyone I read about did not reporting smelling like bleach (or a swimming pool) and, in any case, it is recommended that the person soaking in the bath rinse off with regular water afterward. Also, the consensus amongst people trying out this treatment is that soaking once or twice a day in bleach is needed to decrease outbreaks.