I do not think the cotton had anything to do with the tooth needing retreatment.I see no reason why you should not have had some local anesthesia. I also think that the communication between the professionals was very poor. I think their egos are getting in the way and the concern for the patient is suffering.
the cotton is not the cause for your pain, although it definitely should have been removed when the post or buildup was done. If you did not have a post or a buildup done, then that means that temporary filling material and the cotton ball were left in ypour tooth by your general dentist, which is not up to the standard of care--this may cause the crown to fail, but it is probably not the source of your pain. In my opinion, anesthetic should be used for retreatments of root canals.
The pain could be from the crown being high, from the root canal procedure (root canals are not 100% successful) or something else. like a periodontal (gum/bone) problem or a fracture in the tooth (which is not always evident on a film). Good luck.