This may be due to some fungal infection.
Fungal infection occurs due to poor immunity. To get rid of it we need regular exercise and good nutritious food. Avoid all types of shampoo and soap.
If You have Faith in Homeopathy - You can apply:
Berberis Aquifolium ointment & Azadirachta Indica ointments twice daily after washing and drying skin with pure plane water.
These are good herbal Homeopathic creams for fungal infection for dry skin.
(both medicines are also available in liquid Form (Q) for oily skin - Apply 10% of each diluted in RO water or Distilled water after washing and drying with pure plane water)
You can Also take some internal medicine for prompt and permanent cure:
(1) Tellurium 30 thrice daily for one month.
(2) Rhus Tox 30 Thrice daily for one month
These medicines have no adverse effects if taken under supervision of qualified homeopathic consultant.
For more help before & after taking these medicines you can consult me personally through Practo