FUE hair transplant, a lot of oil coming out of my skin. I had oily skin issues but not that significant. Is it normal?

Ask your doctor to take a look.  Excess oil may contribute to scalp inflammation and there are more aggressive shampoos for this problem.

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  

What you are going through is normal.  It is likely serous drainage from the procedure and a combination of some fluid which was injected at the time of the surgery.  As long as there is no significant redness and warmth to suggest an infection, I would not worry about it at this time.  I do not feel that there is a pathological process of increased oil/sebum production.  The clear serous fluid drainage can last for 7 to 10 days following the procedure.

More frequent shampooing is the solution for oily skin. I believe that the advice given to you by your doctor make sense.