Can braces widen my smile and make my face look rounder? (Photos)

yes, there is a significant change in your profile. but agree with your orthodontist, such changes are not possible only with braces treatment. if you have pre and post treatment lateral cephalogram thn its easy to understand what changes occurred during treatment. another issue is selfie with mobile camera. search 'why long face in selfies' in google and go through it. so compare your pre and post photos taken by regular camera [not mobile phones]. so compare pre post photos taken by regular cameras.

Wow...I see what you mean. Those photos appear drastically different.  Both attractive...just different shapes. Of course braces can affect the width of your smile.  Certain kinds of orthodontic treatment can affect your profile and lip posture, when looking from the side.  But braces typically don't change the overall shape of the face in the transverse dimension.  The cheek bones determine the width above the lips, and the jaw line determines the width below the lips.  There are certain kinds of treatment that are geared toward minimizing downward growth of the jaw, which can create an appearance of a shorter, rounder face height.  But yours appears to be a significant change in a short period of time.  Questions...how old are you (it's hard to tell from your photos)?  Are you still growing? That can make a difference.  Can you show pictures of your teeth before and currently?