Sensitive skin

Hey mamas! Any babies out there with super sensitive skin?? Like I mean can’t put any lotions or anything on this little babe without his skin going full breakout in a horrible blotchy red rash all over his body. It’s to the point where all baths are with lukewarm water only no soap and can’t even put lotion on afterwards so his skin is so dry. It’s believed that he also has total body eczema but can’t put anything on it. What do you do???