Non-surgical Rhinoplasty - is It Safe? Why So Controversial?

Nonsurgical Rhinoplasties are very safe if done properly with a well-trained surgeon.  Seeing a surgeon that understands nasal anatomy, and has experience operating on a nose, is the best way to start.  Next, find out if they use needles or a cannula to inject the filler.  Using needles for injection in the nose is what leads to problems and 'bad press'.  Cannulas are safer though experience with cannula injection is important.  Finally, find a surgeon who offers a multitude of fillers for your nonsurgical rhinoplasty.  Every skin type is different and creating a bridge requires a different filler than filling a defect or creating symmetry.  Thin skin utilizes a different filler than thick skin so having a variety of fillers to choose from is important.

Non-surgical rhinoplasty is a very safe procedure when performed by a qualified doctor. The controversy may stem from the fact that many people are skeptical that correction of the nose bridge can be done without surgery, although the results are not permanent. If you are interested in seeing a real- life example, I am including a link to a patient case from my office at the Dr.U Clinic in Los Angeles. The young lady has a nose-bridge similar to yours and achieved the straighter contour that she wanted with a dermal filler called Radiesse. She also has a video which you can watch.

A non-surgical rhinoplasty (nose job) is a quick 5 minute in office procedure which is performed with fillers to improve the appearance of the nose with zero downtime. I typically improve bumps on the bridge of the nose, make the bridge look more straight and narrow, refine the tip and turn the tip up a bit. The length of the result depends on which type of filler is utilized. 
Most surgeons, including myself, use hyaluronic acid (HA)  fillers such a Juvederm, Restylane or Voluma. The duration of each of this fillers is longer in the nose than those typically quoted, as it does not move as much as other parts of the face. Juvederm and Restylane-L typically last 9-12 months in the nose and Restylane Lyft and Voluma can last 1-2 years.  I have noticed that on occasion, less is needed over time and in some minor cases only a few times of injections caused a permanent change, perhaps by stimulation a bit of scar tissue to fill in the area.  A nice feature of the HA fillers is that there is a reversal agent that will reverse the filler right then and there if you are unhappy with the results (have never had to do this, but it is nice to know that it can be done). 
Blindness and skin necrosis (death of skin) because of decreased or blocked blood flow to the area is a feared risk of non-surgical rhinoplasty. Despite training and experience, which can reduce the risk, it is never actually zero. Luckily this is extremely rare, and when skin necrosis is treated correctly and promptly, it will can resolve. 
Some will use Radiesse, which is considered semi-permanent filler.  One issue with Radiesse is that there have been some reports of granulaoma formation (infammatory response) and it can make surgical rhinoplasty a bit more difficult in the future.  
For these reasons, I prefer the HA fillers and will use Lyft or Voluma if there is enough soft tissue coverage for a longer lasting result. 
Seek consultation with a board-certified rhinoplasty expert for an in person consultation for an examination and discussion of your surgical and non-surgical options. I hope this helps and best wishes.