Can sun exposure 2 weeks after Kybella cause problems?

Sun exposure won't adversely affect your Kybella. My guess is that maybe you did more "exercise" than normal and that is what is causing the swelling. It will resolve with time. However, if you spend time in the sun, make sure to wear a good UVA/UVB sunscreen with a least an SPF of 30 to protect your skin. 

Kybella always induces swelling but a sun burn can add to the swelling. Kybella is in no way phtotosensitizing and your results are not affected by the sun.  I would use a burn cream now to help soothe the area and some cold compresses and Benadryl as well if you are swollen.  Please consult a expert in Kybella for the best cosmetic results.  Best, Dr. Green