Looks like you have developed an allergic rash known as allergic contact dermatitis. Sometimes there may be superimposed fungal infection. Please share a photo so that we can diagnose and give appropriate cream.
Next Steps
meanwhile, try to apply coconut oil after washing your hands with water and drying it properly.
Health Tips
Apply coconut oil at night before sleeping also which will protect the barrier function of your skin. however, the main treatment will be a combination cream which depends on the severity and extent. please share pic for further consultation.