It can be serious

My daughter had to be admitted urgently to hospital
because her eczema was bad and she became very floppy
and ill. I thought eczema was ‘just a skin disease’.
It sounds as though your daughter’s eczema has been very severe.
As you say, many people see eczema simply as ‘just a skin disease’,
but the skin is the body’s largest organ, and it is responsible for
maintaining temperature control and fluid balance. If a considerable
area of skin becomes inflamed and weepy, as seen in eczema flares,
this role becomes more and more difficult to maintain, leading to
water and heat loss from the body. The water loss can occur
through wet, weepy areas of skin or simply via the process of
evaporation from the hot, inflamed skin.
When the skin becomes hot and red all over, this is known as
erythroderma, and urgent treatment is necessary. This is particularly
important in children, who can very quickly become ill from
dehydration as they have a larger area of skin in relation to their
body size so the potential for losing too much water is greater.
Although the skin is not damaged or scarred in the long term from
severe problems like this, the effects of losing heat and water can
be as bad as if your daughter had suffered widespread burns. This
problem is not confined to children: although it is rare, anyone with
a tendency to widespread eczema (usually atopic in type) could
suffer this type of complication.