i hv a little sister who scratches her body everytime.
i had the same issuses. but i use Aveeno products and it helps alot. maybe ur child has ezcema or i-la ( i had that problem when i was younger and i was brought to nigeria and i was told that they rubbed some type of oil/gas on my skin and it helped a little bit.) Even though my skin still gets dry and itchy its not nearly as bad as when i was younger. also u can try not to let your child put things with perfume/ fragance on their skin.
i hope your child's itchiness goes away because i know what i went though.