Does eating on one side of mouth give you an asymmetrical face?

It's possible, but everyone has some asymmetries. Both implants and fillers in the cheeks can create good results for patients.  Both can build up the cheeks or bring symmetry to the face.  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!

This is my expertise and a huge portion of my practice. Asymmetry is normal and expected. Buccal fat pad gives slimming not symmetry. Masseter botox will make you slimmer and make the jawline more loose. Fillers help give shaping and contouring. If you want perfect or close to perfect symmetry you need maxillofacial surgery or implants customized. I suggest seeing an expert to go through all options. Most of my younger clients use fillers to give them shaping especially on the cheeks, jawline, and chin which make the face look more slim and tight; and threads such as PDO or Instalift can build collagen and support the facial shaping and skin looseness over time, slowing down the aging process and given the face a more “snatched” look; and morpheus8 or PiXel8 deep microneedling RF can tighten crepe skin especially on the neck and jawline and is great for long term tightening of the full face, neck and chest; its often used to give the face a slimmer more sculpted look because it tightens the skin and gives lift. an early face lift can be performed as well even in younger clients if they want a different facial shape, maxillofacial surgery with bone breaking or shaving can also be done. For facial slimming a combination of treatments are always needed. Options include: 1. Buccal fat pad removal to reduce fat on the lower face 2. Factite or Renuvion/J Plasma to tighten the lower face, jawline, and chin to reduce fat and give the jawline and neck tightening and shaping. 3. Botox to the masseter to reduce the muscular size of the jaw giving the face an illusion of being more slender 4. Fillers to the jawline, chin, cheeks, temples and brow help to shape the face and make it more angled and defined Always use at home derma rolling (see link to Emerageskin x anteageMD roller plus stem cells/hyaluronic acid ampules) and peels like emeragecosmetics enlighten or aerify that can be used to improve skin quality and tighten the skin while improving wrinkles, pigmentation, acne, and Melasma. See an expert who does facial shaping with surgical and non surgical methods to get a comprehensive option. Best, Dr. Emer.