Will braces fix my bite and help me not have jaw surgery? (Photo)

Oral habits often have underlying causes.  In your case you  have a very underdeveloped maxilla and a small airway.  You probably also have a sever tongue thrust.
Even surgery will fail if you don't correct function.  Form follows function is a basic truth in medicine.Avoid Extraction /Amputation of teeth which can cause development of many new problematic symptoms.
I suggest you see an Oral Myofunctional Therapist or Oral Myologist and work with a DNA Appliance.  Plan on two years of wearing appliance 14-16 hours daily.

You can't do anything until you stop sucking your thumb.  If you don't have the will power, wear heavy gardening gloves or tape your thumb to your pointer finger and tell people it is broken.  Do what you need to do.  It may be the hardest thing you ever have to do, but it can be done.  It is possible to fix your bite with out surgery.  Surgery may be an option but it is always just one of the options available.  Be sure you see a board certified orthodontist.  Beware of dentists who use undefined/meaningless terms such as epigenitic or other such terms that don't have any meaning in orthodontics.