Can Braces Make the Lower Jaw Narrower when There's Extraction?

Just because something theoretically CAN do something does not mean it WILL.  It would help to have photographs to see what you see and offer input.

Think of your upper jaw as a garage and your lower jaw as a car. If your upper jaw (the garage) is underdeveloped then the lower jaw (car) won't fit into the garage. In order to make the lower jaw (car) fit into an undersized upper jaw (garage) you either have to build a bigger garage or get a smaller car.

Your orthodontist has chosen to get a smaller car (extracting teeth). RARELY is the upper jaw the problem when speaking of overjet. Unfortunately, overjet is corrected WAY too frequently by extracting teeth to create space to pull the upper teeth back to mesh with the lower teeth. This type of treatment yields nice straight teeth but does nothing to correct the undersized garage and the car that won't fit into that garage.

Of course the face will change when you move teeth. The face overlays the teeth. I'm not sure why some dentists/orthodontists still believe that a face doesn't change when you move teeth. There have been numerous studies done on identical twins where one twin had extraction orthodontics and the other twin had non-extraction orthodontics and at the end of the treatment they no longer look like twins at all. And guess which twin is more attractive?

Straight teeth alone can NEVER be the only consideration when moving teeth. You only see a person's teeth when they smile but you always see their face. I would much rather give a patient with a beautiful face and crooked teeth than a less beautiful face with straight teeth. The good news though is that a patient can have both a beautiful face and straight teeth if treatment is done with facial aesthetics in mind from the beginning of treatment.

If your lower jaw is retruded your facial beauty is already compromised. To retract the upper teeth in order to match the lower teeth only accentuates that aesthetic compromise because your lips and lower face will also be retracted along with your teeth while your nose and upper face stay in place. In short, your nose gets bigger, your chin remains retruded and weak, your lips become less prominent, your dental arches are narrow (narrow smile with black voids in the corners of your mouth), your TMJ can be adversely affected as well as your airway because of the over retruded lower jaw. 

I hope this long-winded answer isn't overwhelming but I feel so badly for patients who HAD NO IDEA about this stuff and just trusted the advise of their orthodontist. If your orthodontist is suggesting extractions before treatment make sure you get consultations from three other dentists/orthodontists who agree. Once you extract teeth it is extremely difficult and costly to undo and MOST cases can be treated without extracting teeth. 

Good luck!

Extraction of teeth can help in solving a protrusion, when the front teeth are too far forward. With the help of the extraction, the front teeth can be retracted or brought back.  It is unusual for cheeks to appear hallow as you have noticed.  That would imply that the upper and lower jaw is being constricted in the posterior (where your molars are), which is not something we see.  Also keep in mind, that your soft tissue (lips, cheeks) do not move in a 1:1 ratio of how much the teeth move.  The amount of soft tissue change depends on the ethnicity of the person, or what type of soft tissue it is.  So if your top teeth move back 1mm, your upper lip will not move back 1mm, it will be less.  

Braces alone cannot "push jaws back".