Would I Know if I Accidentally Pulled out a Stitch from Rhinoplasty?

Thank you for your posting. When questions arise during the early postoperative period, always check with your surgeon who is in the best position to advise you about your particular case. In general, those sutures visible inside the nose immediately after surgery are absorbable and intended to dissolve over a short period. Although it is uncommon to see damage caused by manipulation of those sutures, It is generally advisable not to pull on them. Signs of damage may include any worsening or persistent pain, bleeding, or change in appearance. Good luck.

We normally close the incisions inside the nse with dissolving sutures. At a week after surgery some of these stitches fall out anyway.  I woud not worry about it. 

Internal nasal sutures usually dissolve and after about a week, they really do not do much.  Most likely it was a chromic suture.  If you are concerned go see your surgeon.