I'm not sure what kind of glue he used but generally with full porcelain crowns, we do use a bond/cement with a curing light. There are cements out there which a light isn't necessary since it is a DUAL cure cement, meaning it can be cured by light or just left alone since it'll cure itself.
As for the swelling, did you take a course of antibiotics? It sounds pretty severe initially so it may take some more time for the healing process to finish. As long as there's gradual improvement, I would monitor the situation.