Tinea Capitis or Psoriasis? (General Medicine)

Medical Case Details:

Hello, I want an opinion regarding my 11-year-old patient having patches on her head (at first, the patch was small and localized, now it has spread all over her head and starting to spread on the upper arm) for several months now—treatment with Ketoconazole shampoo, antifungal cream combined with a steroid. The mother says she is fine with treatment. Once she stops it, the lesions start again. Plus, her head skin gets fine when bathing, but immediately after bathing, it itches severely. No changes in detergents. She was suggested to use gentle baby shampoo-type Mustela gel shampoo. Also suggested running skin biopsy. I was thinking of starting oral antifungal but wanted a second opinion. Thank you in advance.