Yes, you are having contact dermatitis to soap/chemicals in it due to excessive use.
Continuous use of soap for long duration, decrease the moisture of skin, makes skin dry and fragile and easy to break and cause cuts in the skin.
You need to apply soothing skin moisturizer with urea, ceramide base moisturizer to prevent dryness of skin and allergy, immediately after taking bath and everytime after hand wash.
Best step is to stop washing hands continuously for long duration in soap.
Consult your psychiatrist for further help regarding that.
Next Steps
consult or chat with me online for further help
Health Tips
Do not apply any cream/ointment by yourself or from Medical store guy as it might contain steroids or other chemicals which will sometimes damages skin and increase the problem...