You answered your own question -- the splint minimizes the swelling - when it comes off the nose can swell up again. It will go down. Be patient and talk to your doctor.
It is possible to have a unilateral osteotomy if that's what's needed. You need to see a rhinoplasty surgeon for consultation and possible computer imaging. There may be other areas that need to be addressed that you don't appreciate yet in order to get the result you are looking for.
A closed rhinoplasty approach can accomplish narrowing the entire nose with all of the incisions placed on the inside of it. Osteotomies placed in these bones accomplish narrowing them. A tip rhinoplasty is required to narrow the wide nasal tip cartilages. An alar-plasty is required a narrow ...