Newborn allergic to Similac?

My baby is only 4 days old and i was going to only breastfeed him, but he wasn’t getting enough milk so the hospital suggested i supplement formula. So we did, and it was the Similac. Well, i think he is having a bad allergic reaction to it. His face broke out really bad and it’s covered in red patches. He’s also puffy and swollen around the eyes. Took him to the hospital and they keep telling me it’s not the milk. They said he has eczema and the milk is causing it to flair up. She said it should be okay but if i don’t feel comfortable i should switch him over Similac soy. Anyone else ever had this problem with their baby? What should i do?