tbh i am aghast that they would recomend stopping bfeeding! i have sevre eczema myself and was veyr wary that my own children would get it, the eldest has the odd dry bit of skin and had some problems as a baby, including very bad impetigo but i was told by own consultant dermatologist and the allergy clinic that the BEST thing i could do would be to bfeed for as along as possible and if necessary then cut out dairy and obvious allergens from my diet.
i did cut out dairy, which was not to hard, esp as it aggravates my own skin so i never ate much dairy anyway.
i agree with what other posters have said about it not only being diet related but also could be due to house dust mite, pets, pollen, etc, also lanolin is a very common allergy in eczema suffers so make sure not to use any creams etc with that in. do NOT bath you dc very often, it will simply dry the skin out more, even IF you put emollients etc in the water.
other things you can do and probably laready are doing, ALL cotton clothes, bedding etc which you can wash on a high temp to kill of dust mites etc, what washing powder do you use? do you use fabric softner etc? these tend to make eczema worse.
you can also buy special cotton clothes with silver in and organic cotton pjs etc to help with night itching, all these things may help and are worth trying.
sorry this is a bit rushed but am in middle of dinner, bedtime routine etc!
hope you see some improvement soon but i would expect it to take up to a month if not longer and it will be a gradual thing, not a miraculous cure, i am afraid you cant get that for eczema xxxx