My left side of my face is droopier while resting, what can be done? (photos)

 Hi, I have performed many facial shaping procedures using dermal fillers, silastic facial implants (cheek, chin), liposuction and/or facelifts for over 30 years.  From the photos, your cheeks are very flat (concave) in the front, there is some excess fat in the mid face, the chin is weak however there are no signs of "jowls" in the lower face on either side.  Based on these photos and the lack of jowls, you would not be considered a suitable facelift candidate however, the cheeks and chin could be augmented to soften and feminize the face. Following my beauty principles, women look the most feminine, youthful and attractive with heart shaped faces.  Heart shaped faces have cheeks that are full and round in the front.  Cheek augmentation with precise placement of by properly placement of silastic cheek implants (for a permanent enhancement) will create full, round cheeks that will feminize the entire face.
 There are many faces that have excess fat over the cheek area which hides the "true" shape of the cheeks below.  In addition to obstructing the cheek shape, this excess fat will sag prematurely as it is pulled by gravity at an accelerated rate versus a face without excess fat in the mid face.  Removal of the excess fat, with liposuction, is key when properly shaping the cheeks with cheek implants.  I have used this in combination with cheek implant surgery for 30 years.  In my experience these procedures when combined in a face with excess fat in the mid face are extremely safe, effective and reliable in the aesthetic results they produce.  Liposuction can reduce the excess fat to further shape the cheeks and face.
 I have performed many Chin Augmentations using chin implants for over 30 years.  From the photos, your chin is weak.  A weak chin creates an imbalance making the nose appear larger, the mid face top heavy and the lower face look short that de-emphasizes the lips and allows early formation of a double chin.  Chin augmentation using a chin implant will add projection to the chin creating harmony and balance to the lower face. 
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty.  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  In my opinion, you are a good candidate for chin implant surgery.
Hope this helps.