The symptoms you describe may indicate candida infection of either scalp and/or systemic in nature. You may also have gut dysbiosis (pathogenic bacterial overgrowth, candida, parasites, etc.) as well. I would recommend you find a functional medicine practitioner in your area (https://www.functionalmedicine.org/practitioner_search.aspx?id=117) and have a Comprehensive Digestive Stool Analysis performed.
In the meantime for the oily scalp, I recommend Nizoral Shampoo.