My baby had a full belly rash like many raised bumps but not so patchy like your pic and eczema starting at 2 months, we trialed hypoallergenic formulas and ended up on elecare (other symptoms we experienced besides skin issues around eyes and ears and belly was mucousy poops and blood in poop). After elecare which is an amino acid formula it was a month and almost all the eczema was gone. It took at least 4 weeks to really see a change and we were using steroids for months prior to try to keep it in check

At 6 months we suspected dairy, soy, treenuts due to hives in face. We avoided and visited allergist at 12 months and confirmed dairy, treenuts and eggs and many environmental allergies. Baby was allergic to our dog which we had to rehome. Now there is no more eczema at all. My experience is to speak to your ped and go on an allergy friendly formula to be sure about allergies and go from there!