Baby Eczema Solution

My poor baby girl is dealing with some gnarly eczema. She’s been having a continuous outbreak for over a month now (currently 4.5 months old). Her pediatrician said to use some over the counter baby eczema creams/lotions. They haven’t helped. We have given her oatmeal baths every-other-day for over a month, and breast milk baths immediately following the oatmeal baths. We’ve used Aveeno’s entire eczema line of products, and Tubby Todd lotions. Nothing seems to be helping. Her pediatrician says it’s just because of the cold dry air (upstate NY), and sensitive skin. We haven’t changed laundry detergents or done anything like that. Does anyone have a tried and true solution for baby eczema? I’m starting to think it may be an allergy or something and I need to consider adjusting my diet to help her skin…