Eczema itchiness 6 month old

My 6 month old baby has what my gp describes as mild eczema all over her body apart from her face. Her skin can get really dry and I keep her well moisturised throughout the day. The main challenge we have is that she is extremely itchy, if you look at her skin you may not notice the eczema but she is constantly itchy and just uncomfortable most of the time. I'm at a loss I don't know how I can help her and make it easier for her. She is breastfed and I have cut out dairy from my diet and trying to add more whole foods to my diet. Gp keeps prescribing steroids. I initially used it for a couple weeks when she was 3 months old but I don't like the idea of using steroids on her so young and quite frankly I don't think it helped a great deal when I did use it. The itchiness keeps her up at night and irritates her throughout the day. I've changed laundry detergent, no soaps, fragrances etc. I just want to know if anyone has been in a similar position and if there was anything that helped. I'm desperate to help ease her discomfort, I've tried TCM taking herbs myself for a couple weeks but have not noticed much difference and it is quite expensive, not a sustainable option for me at the moment. I'm assuming the irritation is coming from under the skin but I just don't know how to target that. I've tried aveeno creams but anything oat based seems to give her a flare up. I've just bought cerave baby cream so I will try this. Previously tried la Roche posay but not helpful. Any advice or success stories of those in similar situations would really help us! Thanks