I have a large indentation on my right buttock. Fat placement? (photos)

The indentation can be due to trauma or injection. Sometimes people present deep skin attachment that creates a puckering or grooves. In any case, the fat injection can be an option but needs to be combined with deep release of the retaining fibrous band, performed at the same time. It should be followed with careful protection and immobilization of the area for up to 6 weeks. 
Christian Drehsen, MD

Indentations in the buttock area can be caused by various factors, including muscle atrophy, nerve damage, or fat loss, which can sometimes happen after an injection. Given that you're now noticing a similar indentation forming on the left side, it's important to determine the underlying cause before deciding on a treatment.
Fat grafting (or fat transfer) is a common solution for filling indentations and restoring a smooth contour. This involves taking fat from another part of your body and injecting it into the affected area. However, if the indentations are due to muscle or nerve issues, addressing those underlying causes might be necessary for a long-lasting result.
I recommend seeking a consultation with a plastic surgeon experienced in both fat grafting and muscle conditions. They can assess whether fat transfer alone will be effective or if you need additional treatment for any potential muscle or nerve involvement.

 Yes, this is a reasonable option and can work for a host of contour depressions caused by medication, trauma, or disease.  Find a board certified plastic surgeon with ELITE credentials who performs hundreds of fat transfers each year with favorable patient reviews and great results indicated by before and after photos..  Kenneth Hughes, MD, Board Certified Plastic Surgeon Los Angeles, CA

I suggest you see an expert.  This can be improved with fat grafting and stem cell placement over time.  It will need a few treatments and subcision at the same time will help more.  Best, Dr. Emer.

I would recommend fat grafting for this problem.  It may be you received a steroid injection which can cause fat atrophy.  Fat grafting should fix this problem provided  other medical issues are not present.