should I use PropeciaFfinasteride after hair transplant due to shock loss on recipient and donor?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  Taking Propecia after you had shock loss probably would not help. 

Finasteride works by blocking the effect of testosterone derived hormones on the hair follicles. Since the donor hairs from the back of the head are not influenced by these hormones, the finasteride won't have any effect on how well your transplanted hair stays or how the recipient site heals. However, it does affect the original hairs on the top and sides. If you are losing these, I strongly recommend you try finasteride for yourself. Not just for right after your transplant but as a general preventative moving forward. Side effects are fairly rare, and the nearly always go away quickly after you stop taking the medication. 

Finasteride is used to prevent hair loss, but since you've already lost a significant portion of your hair due to shock loss it likely wouldn't help much more. But if you still feel as if you have a lot of hair left that you don't want to lose, it may be worth taking- I would suggest you talk to your doctor about it.

It
is the shock loss on the recipient area that you should be concerned about
after a hair transplant.  However, you
should start finasteride to keep your native scalp hair but only after seeing a
specialist who can map your miniaturization of scalp hair.  The hairs you have in the donor area are
considered permanent hair and are coming from the permanent zone. These hairs
are not susceptible to Dihydrotestosterone (DHT) the hormone responsible for
hair loss in androgenetic alopecia.

In my opinion, the reason to add finasteride is not for any short term benefit this soon after your FUT procedure.  Your apparent telogen effluvium post-operative shedding, should start resolving soon. Finasteride side effects are quite unusual, but taking a prescription medication indefinitely is not a comfortable decision for many young men, especially when it may affect them sexually. It is a long term approach & very effective, but may not show any substantial benefit for nearly a year in many of my patients. I hope this is helpful. Waiting for the results after HT is difficult, but almost always worth the wait for the patient.  Try to relax & continue the LLLT.  You should be close to turning the corner with obvious benefit you can actually see by about 4-6 months in the typical patient.

Hard to say from the photos if this is shock loss, ongoing hair loss or both.  Regardless, finasteride can help with both and help preserve your native hair.  I would suggest a discussion with your surgeon to go over the facts regarding potential side effects and benefits of the medication.

Keep in mind that hair loss is progressive. It is important to get on a preventative regimen. You should switch to an organic shampoo. You can also consider a natural DHT blocker like Saw Palmetto. There are also medications like Finasteride (a DHT Blocker) and Minoxidil (Rogaine) that can be very helpful in maintaining you existing hair, helping to prevent future loss and even regrow some hair. Before taking any medications you should discuss this with your general physician.

Yes, These medications will help prevent further hair loss. Always consult your surgeon to see what they recommend regarding medications.