Fat Transfer to the Lips
There are better options now a days than fat injections. If you don't like the restylane, consider perlane or juvederm ultra/voulma. Fat is unpredictable, some stays and some doesn't. Fat has the ability to migrate and create long term reactions. With the most recent advances in fillers, I'd suggest seeking a filler injector with more experience and forget the fat injections. I wish you the best of luck, Dr. Emer.
Restylane and Fat Transfer
Restylane is a great product for facial volumizing. However, if you want bigger lips you may be better off getting Juvederm injected or Perlane. You can get fat injected now as well since you want larger lips. For the best cosmetic results please find a board certified dermatologist with a great deal of experience with cosmetic facial injections.