A.,
I am so sorry for your little one. Luckily my son did not suffer from eczema, but I DO!
It is a life long battle that was bad when I was a child, got worse during my teen years, and came back after I had my son, and even now as I type this (my son is now two). I am now 26. So you do have a long journey if your son is anything like me. I remember seeing my mother cry for the first time in my life, when she saw how much I suffered as a child from this ailment (I believe I was 6 or 7 years old at the time). Living in FL does not help either, with this recent heat wave!
What has helped me tremendously is washing with fragrance free products like Cetaphil (it is expensive so I use the Walmart brand which is the same exact thing), I use this to shower with as well as a facial cleanser. I've been told Aquaphor is good as well for babies, I have never used it myself. I have used Gentle Naturals Baby Eczema Cream also. They also have a Gentle Naturals Baby Wash you may decide to try. I stopped using Gentle Naturals only because they changed the formula recently, and to me the smell is off putting. They have baby Pooh characters on the packaging, and you can find them anywhere, Walmart, Target, CVS...
Eucerin Original Cream is the best. Costly too! Again I use the Walmart brand in the tub, which is the same thing, but only costs $3 as opposed $15 a pop! Put this cream on right after a bath, don't even bother rubbing it in. The skin will soak it up on its on accord and his skin will be so supple (especially if you did this before bedtime).
RX or OTC cream containing Betamethazone helped me a lot, and more recently my Dr RXed an ointment called Triamcinolone within 3 days my rash was gone.
Ask your pediatrician for a referral to a dermatologist. Only those trained specifically in skin care, I have found, really do the most help (no offense to your ped.)!
Good Luck and I hope your little one can find relief!