The rhinoplasty procedure would involve narrowing the nasal bones with osteotomies, narrowing the nasal tip, and an alar plasty to narrow the wide nostrils. This is a full rhinoplasty, not a tip-rhinoplasty.
You can have just the lower third made smaller as long as u realize the upper 2/3 will look wider, and can be addressed later. See a very experienced rhinoplasty surgeon who is very familiar with AA rhinoplasty.
Congrats on your interest in improving your nasal appearance. You would benefit from a full rhinoplasty including tip work and nasal ala reductions. Cost varies between surgeons. Most of us offer financing options. I would recommend meeting with a few surgeons to get a feel for price range as well as appearance expectations.