From the description provided, you seem to be having seborrheic dermatitis
To treat the same
Avoid oiling scalp
Use a ketoconazole
based shampoo every alternate day. Apply it for 10 minutes then wash off
Apply a steroid salicylic acid
lotion in scalp every night.
Take tablet cetirizine
Once response is seen, stop steroid lotion and continue using shampoo once in a week.
Once dandruff problem will resolve, your hair fall would reduce.
Hope that helped.