M.G.
ETA:
I have heard of the bleach bath - it was not recommended to us, but a friend of mine works on pediatrics team and her old school pediatrician recommends it for eczema - it supposedly clears up the cuts. I don't know.. I would think it would be drying personally. If it's not working for you, maybe take a break from it. We used vaseline too - (we went through everything). The problem with that is it doesn't allow skin to breathe from what I understand. The emollient is what everyone we saw (including allergist) recommended for an all over moisturizer.
One word of caution with the hydrocortisone (if that's what you are using) - my son has white marks where we used it on his arms (worst eczema for him). It thins skin and reacts different to sun. Coat with sunscreen when exposed. We did and still he has marks. Don't mean to alarm you but just something to be aware of and maybe ask about. We used the least amount we could. Might just be my son's skin.
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All our children had eczema as babies - my husband's side of the family has skin conditions as well as allergies. You don't mention if there is a family history. I do not have any on my side so this was all new to me. I get how hard it is to learn about and deal with when your child is affected.
One of my children had very bad eczema when young and allergies - not to food though. We went through a lot of creams, ointments, etc. trying to deal with the skin issues (redness, soreness, etc.) but it wasn't until we got the allergies under control that it cleared up. Pets, dust for us - so lifestyle change and meds.
Not sure about Vaseline? Never heard of that. We used 'hydrous emollient'. Virtually nothing in it except water - awesome stuff. In a tub from pharmacy - don't need a prescription. It's just white thick pasty stuff that coats them but is quite light- you coat them after baths to hold water in.
If you have pets - think about re-homing. It made the world of difference to our child. That and carpet or rugs. We removed the carpet - air purifiers, etc. Hepa filters. There are a lot of changes you can make to your surroundings.
Washing - we used Dove. That's what they recommended- and rinse, rinse, and then rinse some more. Use very little (tiny amount). We used Tide Free (no dye, no perfumes) detergent, and did an extra rinse at the end in washing machine. We also used maybe a quarter of the recommended amount of detergent.
My kids were on antibiotics when babies/toddlers - but so were a lot of our relatives, and they didn't have eczema on my side of the family.
My kids outgrew the eczema over time for the most part (somewhere in elementary school) - even my allergic one except for places like elbows, etc. but it's manageable.
Good luck and I hope you find answers :)