I had eczema pretty bad when I was younger but now I'll only get it around my wrist by my bracelets once in a great while. Instead of hot baths for him try having it on the cooler side & make sure he's totally 100% dry before dressing him. After he eats I'd wipe his face with water & a soft wash cloth in case wipes are irritating it further, & make sure his face dries quickly after that.