Treatment options for inward fold at the ends of my lips? (photos)

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.

A combination of botox and fillers to your midface and corners of the mouth is a non-surgical option. 

The downturn at the corner of your lips is due to early age related volume loss. Exercises will not help and since we can't direct where our bodies lay down fat there is no optimal body fat percentage for this concern specifically. Very slender people tend to show earlier signs of facial aging due to less facial fat, so try to maintain a health body weight/BMI. Fillers to support the oral commissures will address your concern and help maintain your youthful appearance. 

A small amount of filler would help with the volume loss and lines at the corners of your mouth. This is a common indication for fillers. 

The best treatment for the loss of volume at the edges of your lips is dermal fillers.  Dermal fillers can plump under the under the folds and erase the depressions in that area.  Unfortunately, there are no exercises that would improve that area.  Since everyone ages differently, is difficult to give a definitive body fat percentage that maintains facial volume and prevents sagging.  It is true that people who are thin with low body fat can have a loss of facial volume and an "aged face".  It is best to keep your weight in the ideal Body Mass Index range (18.5-24.9).