There are as many opinions as people. I would not choose OoO. I wouldn't want to dump toxins into my breastmilk or fetus. I would stop dairy (for both/3 of you), apply coconut oil topically and keep a food journal for the two weeks trying to find a pattern to the eczema. Skin is a detox pathway, so I wouldn't want to ADD die-off toxins into circulation.
Did you have antibiotics during this pregnancy? Do you have/had any mercury fillings in your mouth? Are you consuming any whole food probiotics?
Topically, coconut oil will help cradle cap and yeast. But, you have to identify the underlying cause. In general, yeast is a manifestation of an imbalanced gut.