Do I need to take Finesteride or Propecia after hair transplant?

You do not have to take Finasteride after a procedure, but it is recommended in most cases. Understand that hair loss is progressive, and Finasteride will help halt this progression.A great first step would be an online consultation. Often you can submit photos to top hair restoration surgeons for a complimentary evaluation. This should help lead you in the right direction. Having multiple consultations with different doctors cannot hurt. 

Also, information such as your family hairloss history as well as your preventative regimen that you are on such as minoxidil use and other topicals would be helpful.

If you are young and still have hair on top of your head, then yes.  If not, you risk losing the hair you still have on top of your head.  Finesteride won't affect the grafts, but you want to maintain as much thickness as possible.  If you are over 60 and your hairloss has been stable for 10 or more years, then maybe not. Ask your doctor.  Good luck!