After reading history and analysing medications given by Skin specialist it seems that your child is having eczema
. This is type of allergic condition of the skin which makes skin dry, rough and pigmented with the time. Child usually out grows of it by age of 6 years. There is no any particular medicine to cure allergy.
The first line of treatment is applying moisturizer creams and when it is not controlled by alone moisturizer creams then low potency steroid creams like fluticasone
needs to be applied daily till it comes under control. Rashes
are usually seen more during winter season. You can keep allergy
under control but can't cure it.
Raised IgE level proves that there is no alternate diagnosis.