Formula and eczema

My son has SUCH sensitive, eczema-prone skin. We have tried a number of formulas including enfacare(for low birthweight), gentlease, Enfamil AR (for his horrible spitting up), and just regular infant.

We tried Nutramigen for a few days when he was a month old, but shortly after he was hospitalized for losing too much weight so they switched him to the enfacare.

Has anyone else had babies with problem skin and bad eczema. He has recently broke out on his back and it looks so horrible. I’m not sure if it’s actually eczema or something else. He also gets red patches on his face and will scratch until he bleeds if I don’t have socks on his hands.

Did a formula change improve rashes? If so what formula helped? He’s currently on Enfamil Gentlease and from what I can tell it doesn’t improve anything at all.