My son has eczema. It's not as bad as your cousin's kid, but he does have dry spots on his arms, legs, and scalp. I use 3 different baby eczema creams (alternating - mostly using the brand with the baby Winnie the Pooh characters), bathe him in Aveeno's baby oatmeal bath at least once a month (letting him soak for 20 minutes), and put a very small amount of Benadryl in his bottles (roughly 1/8th of a teaspoon). The only thing that keeps it under control is the Benadryl in his bottles. I checked with the pediatrician and he OK'd it. I started giving him about 1/16th of a teaspoon in his bottles when he was around 2-3 months old. He also is lactose intolerant, an allergy that is very common in people who have eczema.
I'm not completely sure about this, but I think that eczema is a form of an allergic reaction. An allergic reaction is the body's immune system with a couple cans of Red Bull and a handful of espressos. Having an allergic reaction can weaken your immune system and make it more likely that you will get sick and/or have another allergic reaction relatively soon. My best advice would be to try to find out what triggers the outbreaks and avoid it. If it is necessary to be in contact with this/these trigger(s), I would suggest removing it from your environment and avoiding it completely for a period of about 2-4 weeks. After that period, I would suggest slowly phasing very small amounts into your environment, so your body would get used to it and not attack it, causing an allergic reaction/outbreak. This could take months and numerous tries, but it's worked for me numerous times and the rewards are great.
HTH! Good luck!
(ITA with maree_strawberry, BTW.)