As an oculoplastics specialist (expertise in eyelids and brows and eye sockets), I am aware of sodium deoxycholate injections (the active ingredient of Kybella) into the lower lid fat pads. It is an "off-label" use of Kybella....but the first use of injectable deoxycholate for cosmetic reduction of fat WAS, in fact, on lower lid fat pads!!!! It was done by Patricia Rittes, MD, a Dermatologist from Sao Paolo, Brazil. She even received an award from the European Academy of Cosmetic Surgery for her work! (She was one of my five teachers in these injections.) I do not know why you did not swell under one of your eyes if you were injected there with sodium deoxycholate. The medication kills fat, and the more fat, the more swelling. And the more swelling, the more skin-tightening you will get (as proven by the excellent published works of Diane Duncan, MD, plastic surgeon from Fort Collins, CO, and another one of my 5 teachers in these injections). I recommend you speak with the physician provider about it.