Thanks for the query.
Hair oil is of no benefit in present day knowledge though the massage during a hair oil application may be beneficial. You could be having either Seborrhea capitis or Seborrheic dermatitis from your description. Start using an antifungal shampoo everyday for first week and then reduce the application to twice a week for maintenance. You should keep the shampoo atleast for 5 minutes on the scalp for it to act. This should solve your problem.
Next Steps
However if problem persists, consult a Dermatologist for proper diagnosis and treatment plans.