Did they do any procedures to the gum themselves prior or during the crown treatment? There may be some excess cement that can be left on accident which cause an irritation in the area.
This situation began with a routine crown while I had the temp crown on I developed severe pain. This pain lasted several days and I went to the dentist that decided I had an abcess, I took the antibotics for 10 day but I NEVER had gum swelling until I had the root canal and perm crown. My gums around the new crown are still very tender... :(
The root canal shouldn't have much to do with your gums. Did you have an abscess or severe swelling initially?