Newborn hair & skin care

Alaina

Hello, I have a 2 month old with TONS of hair. Her skin & hair have been seeming a little more on the dry side the last week or so. I ‘m biracial (African American & Caucasian) , my fiance (her father) is African American. So she’s basically African American but her skin is exactly like mine when it comes to sensitivity & color and her hair is exactly like mine too. So at 2m her hair is still barely curled up, Just at the top really with very loose curls. We use aveeno bath products, i’ve used nothing in her hair yet but water and the shampoo/body wash. I have raw undefined shea butter and a tiny bit of coconut oil left from when I was pregnant with her. Can i use these things on her hair and skin?? I know its a natural oil but I ‘m kind of nervous.