I've always removed the nasal splints myself in the office. I am not sure why you need to remove this yourself. One thing you want to ensure is that you do not tug or pull excessively on the splint. I would imagine that a warm shower and running the shower head right on the splint will help...
It's not unusual to have some swelling immediately after a Rhinoplasty. This will continue for 6-9 months to a lessening degree. For specific results, you would need to speak with your Rhinoplasty Surgeon as he/she's the only one that knows what was done to your nose during...
Yes, removing nasal packing will generally make the nose smaller or narrower. Packing type and shape will vary among surgeons and rhinoplasty procedures. If packing is used for your rhinoplasty, then it is typically removed the next day in the office.
Best of luck.
Dr. Chaboki