First kudos to a great parenting ... but eczema comes in a lot of sensitivities, I'll separate a few in below summarize;

1. For head try use sebame so they won't form bad dandruff but consult pharmacy if it's ok for infant this age
2. Use soap which is medicinal
3. Seafood is a no no
4. Tight waist pant, belt metal will cause itchiness - try stay out of it

Lastly I got one friend severe case but he's late 20s or early 30s it comes and go, he went hospital for jap and they wrap him like mummy but it was a good kill for the eczhema.. note that this is better treatment in SG as MY treat it differently

well Idk in details but he was wrap like a mummy and was told jap needed....since then it was like 2 - 3 months after his eczema since to be improve a lot