Thank you for your query on Healthcare Magic.
The spots on her palms are looking like resulted from an allergic reaction
to some allergen.
The allergen may be food, dust, or something which might have in contact withy the child.
Is child having spots on soles and any lesions in the mouth?
For itching you can give a prescribed oral antihistamine like Benadryl
in prescribed dosage.
For externally over skin apply a calamine containing lotion for soothing effect.
Consult your Pediatrician
for examination and for specific treatment.
Hope I have answered your query.