T.O.
Pediatricians know about babies. Dermatologists, unless they are a pediatric dermatologist, would not know all the particulars involving infants. In my oppinion you should stick with the pediatrician and try a different oil, like olive oil, if you don't like the smell.
And add a humidfier to the baby's room. It's winter, the air is dry, it can be irritating.