Hello,
There is no medical condition as such which causes oiliness of the hair. I would suggest you to clean your hair frequently with a mild shampoo (you can use the ones for oily hair) and don’t apply any conditioner on the hair. Also you can shampoo twice during each wash and apply shampoo on the scalp without piling the hair on top.
It makes sense to avoid the use of conditioner as it also tends to make the scalp oily. When shampooing the hair, switch from warm water to cool water after you've thoroughly rinsed away the shampoo. The cool water rinse helps close the pores of the scalp and slow down the oil production. Please do consult a dermatologist if the symptoms persist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
May be you have iron deficiency. Get corrected and you should be fine.