Help 😫 dry baby skin and hair

My 3month old LO is biracial and has a very different skin and hair texture than his big sisters, it has just started changing over the last week or so, so I’m not sure what products to switch to.

I’ve been using Castile soap or cetaphil baby for washing (only using soap 1-2 times a week, water baths the rest of the time) and then cetaphil baby lotion. His skin and hair both feel very dry with this routine :(

What products should I try instead? Coconut oil is not an option because we have a severe tree nut allergy in the house and that’s one of the things she’s supposed to avoid.

SO is no help, he’s bald so he doesn’t have to deal with his hair (his head has been regularly shaved since he was a small child) and thinks Vaseline is hydrating for the skin 🙄