KA:
I have many itchy patients, but I've never encountered someone who only itched on the palms and soles.
PrednisolonePrednisolone
Prednisolone ophthalmic
Prednisolone-sodium sulfacetamide ophthalmic suppresses inflammation, but only while you use it.
I know of skin diseases which affect the palms and soles, like psoriasis or certain forms of eczema, but I don't know of conditions which produce just itch without a rash just there.
I think a more precise diagnosis might be in order. Are you under unusual stress?
Good luck.
Dr. R