Pain and swelling after a permanent dental crown.

Sorry to hear about your pain and swelling.  A tooth that needed a crown is usually a tooth that had prior issues: caries, trauma, & etc.  Therefore it is not uncommon that a tooth with a crown will need a root canal.  I would definitely suggest that you go to your dentist to address your concerns.  Toothache is usually isolated to that tooth or the adjacent teeth.  Based on your description, it might be more than just a toothache caused by the crowns. In any case, go to your dentist to have it properly diagnose. 

With any crown preparation and cementation procedure, there is a chance that the tooth is disturbed enough to affect the nerve and a root canal is possible. Or, there could have been an underlying infection, already there, but there was just no radiographic evidence at the time the teeth were prepared or at the time of crown cementation. What  you describe sounds like one of the nerves of one of these teeth was affected and you probably do need a root canal. I would go to see an endodontist, a root canal specialist, and let him or her check the teeth. If the bite has been adjusted and you have this kind of pain and swelling, that sounds like the route to go.