Postoperative splints on the nose are left for variable periods of time.
Different surgeons try to mobilize the nose with a splint with different philosophies. I generally leave a splint on only three days. I don't think leaving a splint on for considerably longer than that will have any negative impact.
Rhinoplasty and cast
I think that you need to call your doctor's office and see if a nurse or other colleague can help you. Good luck.
How long should post-op rhinoplasty cast stay on nose?
I would say the usual amount of time that a cast is left on the nose after rhinoplasty is about one week. There would be no harm in leaving it on for a few days more. I would contact your surgeon's office and if your own surgeon can't remove the cast, they should be able to refer you to another doctor that can remove it for you.