After three weeks of using a doctor prescribed cream should my fungal infection of the groin area be cleared up?

Fungal inf: Depends on what type of fungus, how severe, what type of cream and condition of patient.

Yes: 3 weeks is enough time for a fungal cream to cure a fungal skin infection and stop the itching and the spreading (the skin may take a longer time to return to a normal appearance). Either the fungus is not sensitive to the cream (wrong treatment) or you have some other cause for your rash. See your doctor.