My husband and my mother both have lived with eczema over the years.
My mother's seems to be worse during heavy alelry season and also during the winter when it is very cold.
My husbands is directly related to stress. His is so bad that at night he wears mittens on his hands to keep from scratching at it.
Both have had reasonable success with creams given by the doctor. Also we have discovered that cooler bath water keeps is less irritating.
I am not reccommending that you dunk your daughter in an ice bath <LOL> but keep the water at a nice temperature.
My husband says it can be painful if it gets scratched open but that mostly it is just itchy.