Why does the left side of my face seem to pull toward my cheek bone? How could I fix this? (photo)

Far more important than the technique is the skill and experience of your plastic surgeon. Choose your surgeon rather than the technique and let them explain why one technique may be better than another.  See the below link on some suggestions on finding the most qualified Plastic Surgeon for you.  Always insist on a board certified plastic surgeon.

Facial asymmetries are typical. Both implants and fillers in the cheeks can create good results for patients. Both can build up the cheeks and create symmetry. You must balance the pros and cons of each procedure and do what you feel is the best decision for you.
Fillers:
Pros: No downtime Reversible Quick
Cons: Temporary More expensive in long run
Implants Pros: Permanent Great for patients with poor bone structure Less expensive overtime
Negative: Risks associated with surgery Possible infection Downtime
I hope this helps.

Everyone has some facial asymmetries. I would recommend volume enhancement using a number of techniques ranging from fat to synthetic fillers which can also be used .to improve symmetry and provide subtle lift. Once facial aging progresses to skin laxity and dissent, I recommend a micro or many facelift. I actually have found that patients who get treated surgically sooner end up looking better longer.
Sincerely, 
Philip J. Miller, MD, FACS
Double Board Certified Facial Plastic Surgeon

You have an underdeveloped left side of your face as it is shorter vertically from the eye down to the jawline so everything seems to 'pull' to that side. A proper workups would include a 3D CT scan to determine the shape /size of the underlying bones from which a treatment strategy can be designed to improve the symmetry of your face.

Thank you for your question and photograph. Facial asymmetry is quite common. If there is a functional rotation of your jaw that your bite is off you might want to consider being seen by an oral maxillofacial surgeon. For the cosmetic improvement, there are several options including fillers, fat grafting and facial implants of various materials that could create more symmetry. In our office we would use three-dimensional imaging of the face, both in the diagnosis, and treatment planning of this condition. Until a treatment plan is rendered, the cost is way too variable to even give a range. Hope that's helpful.

 Hi, the left side of your face is shorter vertically with less volume in the mid face (cheeks), chin and jaw line.  This asymmetry between the two sides of your face makes the face appear to "shift" to the left.   All faces have some degree of asymmetry and your face has an average amount.  My experience, over the past 30 years, is that the level of symmetry "does not" dictate how attractive the face is perceived.  As long as the face falls within a "reasonable" range of symmetry, it's the presence or absence of specifically shaped "key" facial features that determines the level of attractiveness. I have performed many facial shaping procedures using dermal fillers, facial implants (cheek, chin), liposuction and/or facelifts for over 30 years.  Following my beauty principles, men look chiseled and handsome with angularity in the cheeks, chin and mandibular angles.  From the photos, your cheeks are flat in the front (more so on the left), the chin is weak as are the mandibular angles (again more so on the left).  This combines to create an elongated rectangularly shaped face.  The following procedures would create a more ruggedly handsome face.
Cheek augmentation with cheek implants to add angularity to the cheeks and mid face.  Liposuction can be combined to reduce any excess fat to further shape the cheeks and face.
Chin augmentation, using a chin implant, to add projection to the chin creating harmony and balance to the lower face.  I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  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 (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut bone segments).  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.  
Augmentation of the mandibular angles using a dermal filler (jaw implants have too many unwanted side effects IMHO) to add volume, angularity and flare to the jaw line.
Hope this helps.