What are some remedies to expedite the process of getting facial swelling to go down? (Photos)

Swelling is not uncommon after these types of procedures.  I would put yourself on a regular regimen of 800 mg of Ibuprofen 3 times a day with food as long as its okay with your primary physician.  Prednisone, Loratadine (or other over the counter anti-allergy medications) each morning and Benadryl at night can all help.  Low salt diet, try to keep yourself on the colder side, elevate your head when you sleep at night and ice anytime are good measures too.  

Ice compress can be helpful for the first 48 hours. Avoiding exercise and alcohol are a must. Benadryl at night and Allegra during the day can also help. I have had good results with acupuncture as well.
You should not take ibuprofen or steroids because this blocks the healing cascade that PRP induces. 
 The reality is that it can take 4-7 days for this to clear up in some cases. The above will help but PRP causes swelling in order to stimulate its desired effect and under the eye will look puffy with only a small amount of swelling.