welcome to healthcare magic forum,
1)Your problem seems to be due to repeated trauma & dryness of affected part. So please apply good moisterizer over both hands,every time you wash hands.Use only mild soap for cleansing hands.
2)Apply Clonate-F(Combination of Clobetasole & fusidic acid
) cream twice daily over red & itchy skin,during rest time.Gradually decrease the application frequency.