I had buccal fat removal on Wednesday the 12th April. The swelling is excessive on one side? (Photo)

Based on your narrative and photos, you may have a leak of saliva from your right parotid salivary gland into your cheek. Parotid leaks may take a prolonged period of weeks to heal, and you may benefit from consulting with an experienced and reputable ENT specialist.
We have experience with treating parotid leaks after facelift and parotidectomy surgery, but not after buccal fat removal. What follows is not meant to be specific advice, but rather some friendly thoughts from across the pond to try to help you.
The cheek incision for buccal fat removal is just below your parotid duct - the tube that delivers saliva from your parotid gland into your mouth. A disruption of the duct could lead to saliva collecting in your right buccal space. When managing parotid leaks, here are some considerations  
Eat a bland diet while avoiding tart, sour and spicy food that overstimulates saliva productionA compressive dressing on your cheek may help, but may be impractical  to applyUse of antibiotics to prevent infection may be discussed with your surgeon. Medication to decrease saliva production may be discussed with your doctorBotox injections (50-100u) into your right parotid gland to decrease salivary production may be beneficialAllowing the saliva to continuously drain, either internally or externally, may be favorable compared to allowing recurrent collection. If your right cheek feels and looks better when the incision in your mouth was let to drain, consider asking your surgeon to re-open the incision in your mouth and place a small, temporary rubber drain. A drain may function to keep your wound open several millimeters to allow your parotid saliva to drain in your mouth as it is supposed to. Preventing recollection of saliva may be the best way to promote healing by allowing the space that used to hold your buccal fat to close. Allowing salivary drainage freely into your mouth, may be preferred to allowing recurrent salivary collection followed by serial drainages. SeromaCath is a closed, percutaneous suction catheter that may be placed through your skin to drain the saliva. This may not be necessary, but it's mentioned since we have used these successfully to treat parotid leaks after facelift.Let us know how you make out. You can feel free to ask your surgeon to call me. Patience, and close follow up with a reputable physician will be a virtue:)
Thank you, and wishing you well in your healing. Dr Joseph.

Patients with questions and concern about their buccal fat removal healing process should contact the plastic surgeon that performed the procedure to address these concerns and determine if there is need any need of management