Hi, S.! My baby had the exact same problem at age 3 months. His eczema was triggered by Johnson & Johnson's Baby Wash, which I later discovered has harsh chemicals in it. That really ticked me off! Anyway, I started looking at the products in my home and realized that I was poisoning my child. I switched to dye-free, perfume-free, paraben-free, whatever-free products and it helped trememdously. I even use perfume-free body soap, shampoo, and hand soap. I started using "green" cleaning products and use Oxy Clean istead of bleach. I tried vinegar but it made me nauseated! Hydrogen peroxide is a good safe cleaning fluid to repleace bleach. I got rid of all scented candles, Lysol sprays, scented plug-ins. I found that those are just as bad as cigarette smoke.
I also had to change the products that I used on baby. I highly recommend California Baby Baby Wash for Sensitive Skin. It has worked great! I was already using Cetaphil Lotion to prevent my own eczema and started using it for my son. I applied it in 2 layers after his bath and reapplied with Cetaphil Cream every hour or so. What helped my son the most was giving him a bath every day. You'd think this would dry out the skin, but if you keep the bath water lukewarm (91-93 degrees), take him out within 2 minutes, and apply the Cetaphil lotion immediately with reapplication every hour, then you can keep his skin hydrated. I also washed his face and head (affected areas) with warm water in the morning and reapplied the lotion/cream.
The best thing you can do is to stay away from those steroid creams. After I realized that my son's skin was dependent upon the creams to stay clear and that his skin would get worse if I stopped using the cream, I decided to wean my little one off of them. You have to do it gradually. His dermatologist had prescribed this steroid cream and instructed me to apply it twice a day on affected areas. So, after two months of this, I reduced it to once a day, and after two weeks, reduced it to every other day, then every three days, and so on and so on. I then gradually reduced the amount of cream I applied, making the applications thinner and thinner until I didn't apply any at all. You can start by reducing the frequency monthly if your baby's eczema is pretty severe. You have to do it gradually to prevent really bad flareups and throwing your baby's hormone system out of whack.
Also, make sure that his eczema is not being caused by diet. Look for a pattern of flareups. My son's eczema didn't seem to be triggered by anything in his diet but I know that some kids are sensitive to wheat, milk, or eggs, for example.
It seems like a lot of work, but it was all worth it. My son has been eczema free since he was 6 and 1/2 months old, and I started the weaning process and "cleansing" of my house of harsh chemicals at about 5 months. GOOD LUCK with it! Just be consistent and keep telling yourself that "It's gonna work!".