Could not washing hair or applying any hair oil be a reason for hair loss?

I have not applied any hair oil from a couple of months.My dermatologist asked me not to apply any oil on my hair because my skin is oily and I used to have pimples.
But I also stopped washing my hair because i wanted my hair to retain their natural oil if I am not supposed to apply any oil externally.
I have very few or no hair on the sides of my forehead.I used to have hair at those places earlier.Is it that with age we lose some hair from that area? But I am only 19.I also see many people with hair like that.Nothing serious but I am worried now.
What should I do?