Hi isitme1,
I clicked on your link and my DS2 had dreadful eczema just like the baby's cheeks. What worked for us was . .
Scratchsleeves - mits with a sort of back bit so you put them on like a cardigan, and they don't come off. You can get them on a site called www.itchybaby.co.uk . There's lots of other good stuff on there too. (I quite often recommend it because it was really helpful to me, but don't own it, honestly!)
Epaderm - although agree with other posters it seems to be trial and error what works for each individual baby.
Oats in the bath (buy porridge oats, put a handful in a muslin and tie up with an elastic band. Put the bag in the bath and squeeze. At the end of the bath, squeeze out the bag and then wipe it gently over baby. It will be gooey) I agree with not bathing too often too.
We didn't use washing powder or softener but just those eco wash ball type things. I think we got them on little green earthlets site (not sure if it's still going) but you can probably get them anywhere.
Also we used a cream called Hope's Relief (again from itchy baby) which worked wonders for us, but I recently recommended it to a friend and she said it did nothing for her baby! It's very expensive so might not be worth trying.
Even waitrose baby bottom butter, which is £2 I think, worked a little in terms of keeping him moisturised, and not inflaming (think it is just solidified olive oil and camomile)
Definitely try and moisturise at least 3 times a day if you can manage it.
I hope some of this works. The good news for us is that, at 3.5, DS2 is 99% better now. He still gets dry, itchy skin, mostly when it's hot but it's completely manageable. I very much hope your DS2 grows out of it too.