My two have Eczema, all over,and when they were tiny it was on their little faces :(
I now use Aveeno lotion, and Oilatum in their baths. Plus as much as they don't like it, once a week I buff them with infacare in the bath then slap the cream on when they all dry.
Steriod cream is only really used to clear a bad bad flare up, to my knowledge, so we need to be careful using it a long time as it can thin the skin.
I went to the baby clinic rather than the docs with the diagnosis for my babies, & was referred to the skin clinic at my local hospital pretty much straight away. Good luck, it's not nice for you as a mum as well as your little fella.
Ooh and BTW I had wet bandages when I was younger my eczema was that bad, my kids so far have escaped all that, I wish you well, and good luck x