It is really worth bringing this up with your PD before switching or adding any formula, because for eczema babies the cow's milk allergy question is genuinely something that needs a proper assessment rather than a guess. Some babies with eczema do react to cow's milk protein and do better on a hydrolysed or alternative formula, but others are totally fine, so the right answer really depends on your baby specifically. Your PD can refer you for allergy testing if needed and also advise on which formula would help with weight gain without aggravating the skin. Better to get that clarity first before trying different milks on your own, just to be safe.