Sorry to hear about your ordeal. It seems to me that ER used either gut or chromic gut suture. By nature, it will decomposed away. If cut/ laceration was mainly inside toward to your lower dentition, it will go away faster.
As Edge was saying, if it was silk suture, 7 day is about right and that's usual time for post op check up for removal. If it is CG or resorbable suture, and primary closure is not achieved yet, leave the suture. However, primary closure is achieved and loosening thread of suture is bothering you, it should be fine to remove it. Usually, removal is very simple and painless, most of time. I would expect swelling since it was traumatized and cut, I hope that you took some antibiotic to prevent secondary infection. I doubt that you have to go back for 3 times but since I don't know the extent of your injury, it is difficult for me to comment on that. But , most time, one week post op is must to see any sign of infection or progress of your healing.
Again, I wish you fast recovery!