Sadly, I consider myself an expert on eczema...my daughter, who is now 14 mos. has suffered from severe eczema since she was about 4 mos. we pretty much have it under control now, which is good. but yes, if it is appearing in creases, i.e. elbows and knees, those are very common locations for eczema to appear. like you child, my daughter had it all over her face, very, very badly. a combination of things have seemed to work (without the use of eledil, i might ad, which is supposed to have this "black box" scary cancer warning).
first, we only use dove soap when washing her; the plain, unscented bar. anything with perfume or scent seemed to make it flair up, and this included any of the johnson and johnson lavender, etc. this no-scent thing goes as well for the detergent. stay away from dreft or anything that smells. instead, use all free and clear ot something like that.
next, as soon as bathtime is done, when the skin is still damp, apply cetaphil lotion all over the body, paying special attention to the areas that are red.
we ended up having to go to a dermatologist, but this was because her pediatrician just kept telling us to "put vaseline on it" and it got weepy and crusty and started to scar. the dermatologist gave us a prescription for this ointment called desonide. it works really well, it is very mild, and we onlt have to use it if she flares up, which by now is rare.
ok, not here's the kicker. eczema usually has more than one cause, which is why it's so hard to beat. we found that milk also gives her a reaction. she has to drink soy milk and have no yogurt.
so...good luck! please feel free to email me if you have any more questions. i know that eczema is an uphill battle, and there were times where i felt that the pediatrician didn't see the severity of it. (we have a new doc now, and she was the one who suggested the dairy allergy). but be persistant, and know that this is actually something that your baby may outgrow, too.