Anything I can do to facilitate the healing process? (Photo)

First of all, at ten days, you're still very much in the healing process. It may take another week or so for the bruising and major swelling to subside. Apply warm compresses to the involved areas 3-4 x's/d for 15 mins at a time. There does appear to be some asymmetry in the chin implant area with the right side being more prominent than the left. Contact your surgeon if it persists. Sometimes, the implant can buckle on itself creating that fullness laterally. The hardness and the speech should self correct once the swelling subsides and the healing progresses.