My nose looks puffy, swollen, and wide. How long does it take for it to look less puffy and wide? (photos)

Thank you for your question and photos but 18 days post op is way too early to judge your final result.  It literally takes a year for all the swelling to leave the nose.Dr Corbin

Patience is key. It may not feel like it, but 18 days is still very early in your recovery process and you've got a lot of healing left to do. Your swelling will continue to go down in the next few weeks, but it can often take several months for the swelling to subside completely. While I've never evaluated you in person, I can say with confidence that your final result will look very different than the photos you've provided. Best of luck to you as you continue to recover! 

Rhinoplasty takes weeks to months to completely heal.  You most likely will have swelling over this period, but it should become less and less noticeable.  18 days is extremely early in your healing process.  Just follow the advice of your surgeon and give it some time.