Is Surgery the Only Solution to Fix Mandible?

Many cases with an overbite and a recessed lower jaw are mistakenly diagnosed as a problem requiring surgery to bring the lower jaw forward, where the actual problem is that the lower jaw has become "trapped" behind the upper teeth during development and ends up "displaced" back-word out of an ideal position.   This ultimately can lead to TMJ Dysfunction and even Obstructive Sleep Apnea in later years if the problem is not addressed correctly at your age.  Make sure the orthodontist is taking TMJ Tomograms at minimum, and can show the lower jaw (condyles) in a normal position.  If they don't understand your concern, get another opinion from an orthodontist/dentist who works with TMJ Dysfunctions.  They may see the problem as it most likely is, that of the lower jaw is being "trapped" into its recessed position and will work to see that it is brought forward into an ideal position, eliminating the need for any surgery.  I hope this is helpful and that you seek truly an expert opinion on this tricky problem.  After-all, you can't undue surgery, except by another surgery!

Really impossible to know. 
Almost everybody has some degree of skeletal disharmony, but only the most severe require surgery.  Many of the moderately severe ones can be treated either way depending on how much compromise you are willing to accept.  Get a 2nd opinion from an orthodontists (not an oral surgeon) before you agree to surgery