Can Non Surgical Nose Job Correct Exposed Nostrils?

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 purposes.
I've attached a link to a photo demonstrating nostril-lowering with Injectable Fillers.
I hope this is helpful, and best regards.

Non surgical rhinoplasty is most useful for camouflaging a hump on the nose, or a depression in the upper nose. Filler injections are much less effective in correcting nasal tip problems. The risks for a non surgical rhinoplasty are relatively minor. The biggest drawback for such procedures in the need for repeated injections on bi-annual or annual basis.

Rhinoplasty can be taylored to your needs and the appearance of the nostrils can be improved.  If this is a concern, a non-surgical rhinoplasty is not the answer.