What should I look into getting done to fix lip drooping/fat pockets under lip? (Photo)

Based on your photos, you appear to have a pleasing lip appearance, and the pockets beneath your lower lip are not likely fatty and I don't think there is anything that can be done about them. Your facial profile appearance shows a somewhat retrusive, or weak chin appearance. Perhaps permanent non-surgical chin augmentation might help you feel more secure about your facial profile appearance. I hope this is helpful! Sincerely, Dr Joseph

For unique cases where a variety of modalities could be used to treat the condition, I would suggest an in person or virtual consultation to develop a custom and effective treatment plan. It is difficult to precisely define the best option without collecting the same information. I suggest reaching out to an expert for a consultation with surgical and non-surgical methods to get a comprehensive option. Best, Dr. Emer.

Soft tissue issues around the mouth often have a skeletal issue as the fundamental inherent problem. It’s unlikely simplistic solutions are going to give you great results. To get an accurate understanding you need to first get an assessment of facial bone structure. For that I suggest consulting with oral surgeons or plastic surgeons with a craniofacial training background.
Fillers and Botox are probably not going to give quality solutions.
Best,
Mats Hagstrom, MD