Dry Eczema

Remember that creams and lotions can be drying and that heavy, long term use of oils can cause the skin to produce less natural oils.  Soap dries the skin and so does even water.  Preservation of the natural oils is best.  I don't use soap much anymore at all; I use water. You can even use yogurt to cleanse. Remember also that soap residue in clothes dries the skin, so use less detergent and try double rinsing the clothes.  You can even coat the skin with oil before you shower to help protect your oils.

Calcium, drinking enough water, getting your essential fatty acids and lecithin and enzymes to break down the fats will also be helpful.  

When you google "diary oily skin," there are many web sites that say avoid dairy and red meat, because they are loaded with saturated fat and will make your skin oily.
 

Weepy Eczema

Nothing seemed to help the weepy patches of eczema better than zinc oxide ointment.  It dried the eczema cuts on my hands (seems like overnight).  When my face was having an allergic reaction, zinc oxide ointment took care of stopping the golden drops from oozing out of my face.  (My cheeks first became tingly, then bright red and then oozed.) I avoided soap on my cheeks and used cool water and zinc oxide ointment. However, staph craves the metals zinc and manganese.

Remember, though,  that external bacteria and fungus can be a reason for rashes, as was the case with my hands, eyebrows and hair.  Using a toner on the skin to restore the proper pH will help fight infections.