Can a nonsurgical nose job reduce nostril width?

As a rule neither fillers nor neuromodulators like Botox will help a very wide nose. However, under certain circumstances, a couple of droplets injected appropriately into the sides of the wings of the base of the nose can soften the dilator muscles of that region and hence help to narrow the base of the nose. Likewise if there is a bump or hump at the bridge of the nose, injection and straightening of the bridge of the nose with an injectable filler can help to secondarily narrow the lower portion of the nose as a result of the upward pull. Both technqiues are very advanced injection techniques and should not be left to the hands of novice, inexperienced injectors accustomed merely to treating simple smile lines with fillers or for using Botox for the "eleven lines."  Best of luck to you. 

The best way to narrow the nostrils is using a very simple surgical technique called alar wedge excision.   a crescent of nostril skin is cut out where the nostril meets the cheek. The nice thing is that it can be done under local anesthesia and takes less than an hour. It requires minimal recovery and is much cheaper than a full rhinoplasty.