@jack_sdb While I hear that you’d like to get to a root cause, you should know that you may never get there, and open active eczema flares need to be healed as soon as you can to avoid long term consequences.
Especially as a baby being exposed to the world, the first time new potential allergens are encountered, that exposure needs to be through the gut and not the skin/bloodstream (or lungs).
An area to research is the “atopic march” where infant eczema can lead to food allergies as a toddler, asthma in childhood and eventually autoimmunity in middle age.
I would use steroids at the first sign of a flare and by doing so you can stop it and use less overall than being retroactive. Then go on to have a good routine of mild soaking baths, immediately using a bland moisturizer cream, and cotton PJs. In the morning use an occlusive cream (Vanicream or Cerave healing ointment or aquaphor) on all exposed skin and active flares.
I would stop using your homemade soap (do you know the ph of this?) and instead wash with water and a non-soap cleanser like Cetaphil gentle cleanser. In general natural products are another potential allergen. Sorry. Nature is awesome, but awesome in the awe and fear sense not everything is happy sense.
