Accidentally pulled out stitch 1 week post septoplasty?

It is likely that you caused no harm a week after your procedure since the sutures used in septoplasty procedures are usually dissolvable. That being said, I would discuss your concerns with your treating surgeon just to be sure.

If you are a week out after your septoplasty, things should be pretty stable at this point and a broken suture should not cause any significant issues. The one exception would be if you have splints that are sutured in the nose and this was the suture holding them in place, they may be mobile now. Many of the sutures often placed in septoplasty are absorbable, and as they break down and the knots dissolve, you will sometimes see the long end of a suture. If it is hanging out of the nose you can usually carefully trim the excess that you can see so that it is not bothersome. However, I would definitely check in with your surgeon to let him or her know, since not everyone does this procedure the same way or uses the same suture materials. 
Best wishes,