Non-surgical Nose Job to Make Nostrils Smaller and Raise Tip?

Non-surgical rhinoplasty adds volume to the nasal dorsum (nose bridge).  When well performed these can look amazing.  In our clinic we usually use a filler such as hyaluronic acid (ex: juvederm/voluma/restylane/perlane)

Injectable Filler treatments may be very effective in lowering your nostrils without the expense and downtime of a surgical procedure. You should consult several board-certified dermatologists or facial plastic surgeons experienced in the art of injecting fillers in the nose for cosmetic...

The answer is probably yes. It is impossible to say anything without consultation. I advise you to discuss this with your board plastic surgeon, check actual before & after photos ( not the ones made with computer animation programs). 

Generally the area you are referring to needs to be surgically modified.  But you should get evaluated by an expert in surgical and nonsurgical rhinoplasty so they can determine what is best for you.

Having nasal surgery under local anesthesia isn't non-surgical. A non-surgical Rhinoplasty refers to injecting the nose with a tissue filler. Its also called injectable rhinoplasty or the 5 minute nose job (although it usually takes 20 minutes!).