I., I'm so sorry you're having to deal with this - it's hard when something's not right w/ our babies and we have to play detective to get to the bottom of it.
Though your son's eczema might be caused by something else, I'll share with you what our experience was. I have an almost 9 month old son who from 3 weeks old onward had horrible eczema on his face. At first I just thought it would go away, like baby acne or something. But it got worse, more red, more crusty. Our ped suggested lotion, too, then hydrocortisone + lotion, then maybe some other prescription topical lotion... but my gut told me that lotion wasn't going to fix it. We tried the lotion, but nothing prescription, and I kept reading things and asking around. Finally I read about food sensitivities & allergies, asked my ped about eliminating dairy (one of the biggest culprits) and he said it certainly couldn't hurt to try that. Well, it turned out that my little guy was (and still is) allergic to cow's milk protein (milk, butter, cheese, yogurt, anything w/ casein or whey in it). I breastfeed my babies, which meant that *I* had to cut *all* cow dairy out of my diet - and I did so starting when my son was 5 weeks old (and now he's almost 9 mos) - and his face cleared up within a week, his sleep improved *drastically* (more than 20-30 minute stretches, able to be put down while sleeping) and he became happier and much less fussy. [Stop reading here if you don't want to hear about baby poop!] His pooping improved, too - before he was explosively gassy w/ sometimes green and mucousy poop, and he just seemed uncomfortable (bunching up, seeming crampy) a lot of the time. I was pretty surprised that dairy was the culprit - my daughter had no problems (and I breastfed her, too) like that at all.
Again, I have no idea if cow's milk dairy is the culprit in your case, but food allergy in general is certainly worth looking into. Sure, it's a bummer to have to give up cow's milk products, but it's really worth it --> it's *so* much easier to parent my baby when he is not reacting to dairy. He's really much, much happier & healthier. Even though I miss my yogurt and ice cream (I love dairy!), I remind myself that it's such a short period of my life (a few years at most) and my son has a much greater chance of outgrowing the dairy allergy if I don't expose him to it (either through my breastmilk or by giving him anything w/ dairy) until he's 18 mos or 2 or 3 yrs old.
Also, a note about most (but not all!) pediatricians and pediatric specialists - it's worth it to ask about dietary modifications, elimination diets, etc., FIRST instead of going right to prescription medications. Why? Because if the problem is food, the prescriptions would just try to alleviate or mask the *symptoms* not actually correct the problem itself. For allergies, the key is to *remove* the substance from the diet so that the intestines, skin, etc. can heal. But a lot of folks just want something fast, like a cream, to fix it - sure, it's tougher to dig deep and find out if it's food, but in the end I think it's worth it.
Anyway, for more info, check out Kellymom.com which is a fantastic, evidence-based site that provides information and resources for breastfeeding moms who have babies w/ dairy or other food allergies:
Hope that things get better soon, that you are able to find some good answers, and that your son's eczema goes away!