Why is one side of my mouth bigger than the other? What can I do to fix this? (photos)

You would get a nice improvement with lip fillers (Volbella, Restylane, Juvederm). You'll want to see someone meticulous. Nova threads can be used to improve lift and shape. Implants or fat are alternatives. I recommend getting a formal evaluation with a facial sculpting expert to go over your desired results. Best, Dr. Emer

Dear lizzygirl98,I perform a lot of lip injections with fillers such as juvederm and it works great. Many times I need to put more in one side than the other to attempt to even out the vermillion border (The red line of the lip). This helps provide more symmetry at times. I would recommend finding a plastic surgeon to perform you lip injections. Most of my patients have results that last at least 6 months.
Daniel Barrett, MD, MHA, MS 
Certified, American Board of Plastic Surgery  
Member, Am. Society of Plastic Surgery  

Everyone has some asymmetries. Lip augmentations with fillers is a great option to improve the fullness, suppleness and symmetry of the lips. I prefer to use a micro cannula to inject the lips to prevent bruising. Look for a cosmetic dermatologist or plastic surgeon who is an expert in fillers. 
I hope this helps.