Sound like it could be an infection. Speak with the vet about using Malaseb™.

One of the causes of hair loss and itchy skin is a fungal infection called ringworm.
It’s important that you speak with your vet about your pet as this can also spread to people as well. Malaseb can help both treat your pet and reduce contamination in the home if it does have ringworm.

ACVM, No. A7641.