It is standard practice to place a splint on nasal bones after the repair of a nasal fracture. Unless the fracture just occurred, and there is little or no swelling, repair of a nasal fracture is usually performed 5 to 7 days after the trauma when all of the swelling has resolved. If there is bleeding into the nasal septum (a septal hematoma) then immediate drainage of the hematoma is indicated because the septal cartilage blood supply may be compromised resulting in a nasal septal perforation internally, and a "saddle nose" deformity of the external nasal dorsum.
If your nasal bones were actually broken, and the surgeon said that the bones were being reduced with the "tool", then a splint is indicated. This is to prevent external pressure from displacing the bones. If a hematoma was drained then no splint is needed. Your sense of smell may be decreased from your recent fracture, but something smells a little "fishy" to me.
Discuss your concerns with your surgeon.
I hope that all goes well with your healing process. Be well.