Isabelle has eczema and had cradle cap early on. I used Moo Goo Infant scalp care on her cradle cap and it cleared it up completely after 2 applications and now after literally spending hundreds of dollars of products like Gaia, Avado, Emu Oil, Avocado Oil etc I now use good ol baby sorbelene or the Keri moisturiser on her eczema. We use cortisone that has been prescribed if it flares up and use it just for a day and then back to the creams. The key with eczema is to keep the skin moisturised all the time, and sorbelene with glycerine helps do that.
She had the little spots too for a few weeks early on that passed but the eczema stayed.
Good luck hun.