Can I wear a plastic ring in my piercings during rhinoplasty?

As long as they are not metal, it usually is safe to leave them in. However, I would suggest that you discuss your concerns with your plastic surgeon who should be certified by the American Board of Plastic Surgery and ideally a member
of the American Society for Aesthetic Plastic Surgery (ASAPS) or facial plastic
surgeon (otolaryngologist) that you trust and are comfortable with and follow her or his instructions. 

Piercings can be lost, get caught on things, or cause electrical arcs if cautery is used. If the area in the nose is operated on then the plane where the piercing penetrates can be closed during surgery. I will have patients remove piercings or place tape over them if they are not easily removed. Better safe than sorry is the prevalent attitude with piercing. I will replace the alar nosering at the end of surgery if it is not in a plane that was operated on.

First of all, it is important or move all piercings in the nose prior to the rhinoplasty procedure and keep them out for 6 months until full healing has been accomplished. Many surgery centers have rules  about body piercings, so it is best to check with where you having your procedure performed