Small fat pouch on each corner of my mouth. I'm 44 years old. Dermatologist recommends Sculptra, but I'm not convinced. (Photos)

Based upon the pictures you gave, I would start with a HA filler (Juvederm/Beletero) in the corners of the mouth.  I do notice that there is some of loss of volume in the cheek area which can be treated with an HA filler.  This would help to lift the cheeks and will help to lift the corner of the mouth as well.  It is possible to use the Sculptra to build the collagen but I like it in the periauricular area (area before the ear near the jawline - this helps to lift the lower part of the face which also affects the marionette lines).

Sculptra works as a great stimulator for your body to make collagen.  It can often be used to restore some of the fullness in the face lost with age or weight loss.  When your face loses volume, it can cause jowls or other unwanted puffy areas in the face, as skin accumulates in different areas. Based on your photos it is really difficult to assess your face as a whole, since you only included this limited view.  If you have much flatness above, and these puffy areas are resolved with some lift above, it is possible you may get some improvement with a filler like Sculptra.  This would be difficult to assess without an in person evaluation.Seek a surgeon certified by The American Board of Plastic Surgery to get an alternative perspective on your issue.

I agree with your Dermatologist. It appears that you have volume loss in the mid and lower face. Sculptra, my stimulating your body to produce more of its own collagen, will help address this volume loss. The Sculptra could be injected into the midface and temporal lateral fat pad to help give the skin this support.