So sorry for your poor little DS - and sorry for you too. A really tough break for you both.
I'm a long-time eczema sufferer - it's a bugger. And I've passed it on to my daughter
Loads of good advice already. A few extra bits from me:
Baby wipes & handwashing can irritate. Try to keep one warm wet facecloth on the go for clean up.
Short nails. Short as possible.
Someone mentioned tomatoes irritate. Also, citrus juices - not ingesting, but coming into contact with them physically. Lemon/orange juice on my fingers causes a flare up within hours, so try to hold off giving him mandarin segments, etc.
Don't fear steroids. The stronger, the better. My GP said I could give my daughter a short blast with my own medication (betnovate) to try and get a particularly bad patch under control. Thankfully, it worked. What do you want to do is get a flareup under control asap, then move to a maintenance routine. Appreciate others have a different view here - I'm just telling you what worked for us.
The good news from my end is that dietary restrictions have zero impact on my eczema (again, all individual). The bad news is that cat hair is definitely my biggest trigger.
Good luck.