Can a Non-surgical Nose Job Make my Nose Bigger or Wider?

Sure they will. Adding a tissue filler can enlarge a nose, while only surgery can reduce it. Small changes work best using a non-surgical Rhinoplasty.

In general, you can have the height of your nasal bridge increased with an Injectable Filler treatment. For example, if you feel that the bridge of your nose is too curved, then you could have the area filled to provide a straighter appearance.
You should consult a board-certified facial plastic surgeon experienced in the art of using Injectable Fillers for nasal enhancement. You should view many photos before you proceed.
I've attached a link to my Non-Surgical Rhinoplasty photos for your perusal.
I hope this is helpful for you.

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Depending on the areas to be treated there are methods to widen or "strengthen" the profile of the nose using fillers which is also known as the "non-surgical rhinoplasty or nose job". There are risks to all of these procedures and these should be discussed with your surgeon.