Does closing an open bite with braces change your facial shape?

Again, consult: an orthodontist to answer this for your specific problem.

Yes: Your teeth support your lips. Changing the position of the teeth will change the appearance of your lips and face. How great this change will be depends on your individual case. Your orthodontist can give you guidance. Some can even show you computer generated pictures of your face to show you what they expect the changes to be.

Yes: If the orthodontist is changing the position of the teeth, it will change the appearance of your lips and face.-- this change will be for the better BTW!

Yes: Changing position of teeth may change the overlying facial drape. Major changes, however, require changing size, position, and relationships of the bones in your face. At 16 you probably have completed facial growth, and major facial change may require jaw and/or plastic surgery. Start with an Orthodontic Specialist who has the training and experience to manage your reconfiguration.