Maybe it's time to revisit the allergist. It sure sounds like there's another allergy showing up, but I'm no doctor, just a mom and grandmom.
You said the eczema seems to flare and then get worse. I'd keep a journal to keep track of that and help find any triggers. There are many posts you can refer to about
food journals - see the search box at the top of the page.
This problem can be as simple as hay fever:
Do you have locust trees around?
Putting lotions and creams on the eczema might just be the wrong thing. Read the ingredients, especially the "non-active" ones. A lot of people have problems with additives and preservatives. I'd have the kid put on something very simple, like plain old Vaseline or Original Chapstick which might stay on longer. I've used that on kids with allergic eczema around the mouth; it needs to be used several times a day and especially at night, helps keep the kid from licking the lips and making it worse. Give it to the kid to apply himself when he feels the slightest irritation.
Seriously, keep the journal. Anything you can do to help the doctor! Since peanuts and soy are both legumes, has he been eating any others? Peas, beans, lentils? Is he eating the school's lunch? Soy and relatives would be a big suspect for contamination - filler for hamburgers or pizza and pasta and yogurt. "http://www.soyconnection.com/soyfoods/index.php
"U.S. National School Lunch Program uses soy-fortified pastas with 15 to 17 percent protein content."