At his young age, the eczema is almost surely a red flag for allergy. Regardless of whether you are feeding him formula or breastmilk, by FAR the most common allergen for babies is cow's milk protein -- formulas are based on cow's milk, and breastfeeding mothers who eat/drink cow's milk products can have cow's milk protein pass into the breastmilk. The only real way to "test" or "rule out" whether a food is causing an allergy is to remove it from the diet for a minimum of 3-6 weeks (if formula feeding, a temporary switch to hypoallergenic formula, and if breastfeeding, the mother removing ALL cow's milk products for a month) and see if the symptoms go away. Then you do a "challenge" where you give a dose of the cow's milk protein (either 1 bottle of cow's milk based formula, or the breastfeeding mother has a big glass of milk or bowl of ice cream) and watch for the return of the eczema.
My son had the eczema exactly as you describe it - at 5 weeks old, his poor little face was so red, rough, dry, and rashy that he would rub his face back and forth on our shoulders as we carried him because his poor cheeks were so itchy. Our ped, too, suggested lotions or even meds like Zantac, and these would have been RIDICULOUS for our son -- within 7 DAYS of my removing all cow's milk proteins from my diet (I was exclusively breastfeeding my son), the change was AMAZING in my son!!! His face became clear, creamy, smooth, and beautiful. His sleep improved DRAMATICALLY. His fussiness and gassiness and smelly, greenish poops changed into those barely noticeable creamy-yellow breastfed baby poops.
Now, cow's milk proteins are the most *common* causes of allergy in young babies, followed by soy (so be careful of giving your baby soy formula during the test for cow's milk sensitivity because 50% of cow's milk sensitive babies are ALSO sensitive to soy!). But it can be other things as well... wheat or eggs or nuts, for example. Or it could be chemical, as another mother said already in her advice (laundry detergent?). Because the eczema is on your son's face, I would suspect food. If he is on formula, please investigate putting him on hypoallergenic formula for at least a few weeks to see if that helps. If you are breastfeeding him (actually, I think this link has good info regardless of whether he's getting formula or breastmilk!), please check out this excellent link:
http://www.kellymom.com/babyconcerns/food-sensitivity.html
Best of luck to you -- and congratulations for trusting your instincts that the creams aren't really helping and that there's something BIGGER going on that can be identified (allergy) and likely resolved (removing the allergic substance from your son's environment).
Hope this helps!