http://www.nationaleczema.org/
I have not known nor seen, Eczema spread like that.
My Mom has Eczema.
And her's, itches.
Eczema typically itches and is irritating.
Was your child sick recently or with a fever???
If so, then usually after the Virus leaves the body, a B./child can get what is called a 'viral rash' which basically the virus & toxins of the illness, leaving the body. It is small red bumps... and is usually NOT itchy or irritating at all.
It just looks, irritating.
Both of my kids, when young/babies, had the viral rash, after being sick and with a fever.
This is per our Pediatrician.
The rash, self-resolves and goes away.
It can cover, quite a bit of the body/torso.
I tend to doubt, your child has Eczema.
But I am NOT a Doctor.
Next, it was a Nurse that 'diagnosed' your child.
NOT the Doctor him/herself.
Thus, you really need to see a Doctor. And get a proper diagnosis.
Or, she is having an allergic to something topical or ingested or touched.