I don't know what you are seeing, other than swelling, which is also normal. The sensation, whatever specifically that might be, is also normal. Sometimes the instruments that they put in your mouth will rub on those soft tissues and make them bruised or sore, which goes away. Also, the nerves that serve the teeth go to other parts of the face, and a lot of times after a dental procedure various parts of the face will tingle or feel numb for quite sometime. I got a shot for one of my top incisors, and my nostril on my nose was numb for a couple months, but it went away eventually. Put a little gloss or chapstick or vaseline on there, to keep chaffing at a minimum. If there's a little tear or tiny bump, you can dab some hydrogen peroxide or a very light amount of other healing cream on that spot, to help it heal faster. There is also a dental forum at this website, where you can post, only be sure to tell them what the sensation feels like and what the place looks like!
Thank you for your question. I think this will resolve within a week if your doctor has already examine you and not seeing any major concern. But if this aggravates by the time, this may be Trigeminal neuralgia in addition you have typical one sided facial pain extending to temple and eye( ophthalmic branch of trigeminal nerve may be involved) and sore gums of the teeth of same side (maxillary branch of 5th nerve). Trigeminal neuralgia may have a triggering factor like recent history of tooth extraction, touch, cold breeze or hot sensation etc. which you need to evaluate and avoid. Therefore, I would advise an oral medicine specialist consultation or at least a physician to confirm this diagnosis and get you treated accordingly. Take care.