As a result of bells palsy and synkinesis, 1 side of my face lacks tone. Is there a filler that lifts versus creates volume?

Thank you for your question. Fillers are good options as well as PDO threads, which lift the skin. We use these threads in two different ways:
Smooth threads are inserted vertically and horizontally by means of a cannula. The mesh pattern of the threads serves as the foundation for new collagen production as your skin reacts to the sutures by repairing itself around them.Barbed threads are used to produce immediate and dramatic results. The threads are inserted under the skin and grip the skin underneath. When these threads are pulled, they tighten the skin from within, resulting in an instant lift.  Again, collagen production is stimulated as the skin heals itself around the threads.
Ultimately, you'll need an in-office consultation. 

This is difficult to answer without pictures. Volume and contouring of the cheeks can be created with well-placed fillers (Voluma, Radiesse, Bellafill) and Sculptra. Implants or fat are alternatives. Ultherapy, J Plasma and rf treatments can provide skin tightening and lift. I recommend getting a formal evaluation with a facial sculpting expert. Best, Dr. Emer

It's hard to comment on your case without seeing a photo or evaluating you in person. That being said, certain fillers, those with high G', tend to lift. Radiese, Restylane Lyft, and Restylane are high G' fillers. Other fillers such as Juvederm Voluma and Restylane Defyne tend to be better at volumizing. The best thing to do is schedule an in person consultation with an experienced injector to see if you are a good candidate for treatment. In patient's with face synkinesis, neuromodulators like Botox and Dysport are also useful when trying to improve symmetry.