Is it harmful to use oil after 1 months and 1 week after hair transplant?

Given the stage your at after hair transplant i.e. 6 weeks there is no issue with using oil. Both organ and coconut oil are fine to use. In fact a lot of my clients at this stage prefer to use oil in order to reduce the itch and dryness that may occur. It helps sooth the scalp. All the best. 

Hello, great question.  I’m sorry to say you were misinformed by the Clinic where you had your transplant. There is no reason why you can’t use oil at this point in time. Good luck to you.

Just guessing, they may have warned you against excessive usage, as no hair transplant clinic with a doctor should tell you to avoid using oil.
But I have seen many cases where former patients used oil in excessive amounts and on top, they weren't washing their hair everyday. So eventually it caused clogging and dried oil on scalp was coming off uncertain times in flakes. This is something you need to avoid and apply the oil only in small amounts.