If you wished to just narrow the nostrils of your nose, you could do an alarplasty. This would make the nostrils less wide. it could be done with local anesthesia in the office.
To narrow a wide nose requires osteotomies placed in the nasal bones to narrow the bridgeline. To narrow a wide nasal tip requires a tip- plasty. To narrow wide nostrils requires and alar-plasty. An a lar-plasty procedure can be performed under local anesthesia, while a full rhinoplasty is performed under general anesthesia. For more information and many examples, please see the link and the video below
Personally, I don't think your nose is too big, but there are some procedures that can narrow your nostrils and the scars are minimal. The scars are just on the outside of your nostrils in the little crease and heal very well. Good luck!