Did I have a reaction to anesthesia at the dentist? I have a swollen cheek and eye. (photo)

I assume the filling was done on the upper arch.  It is very likely you have a hematoma, basically and internal bruise.  There is a network of blood vessels in the area the dentist gave you the anesthetic.  If the needle enters that area, which is very easy to do, it can cause the burning you experienced followed by localized swelling.  This is best treated with cold compresses and ibuprofen though it would be best if you were monitored by a dentist.  I would return to your dentist to be evaluated.  The dentist did nothing wrong.  This is seen in all practices and usually resolves in a few days to a week.  Good luck!