Gosh Lilith, it's really difficult to inform you specifics unless we see you in person or see your cephalometric radiograph. But what an orthognathic surgery involves is that the bony structures around your mouth have to be corrected to fix your bite and improve your esthetics. Unfortunately, Orthodontics alone will not correct the malocclusion alone.
You can be any of the following:
Class II malocclussion (no chin)
Corrected by:
Mandibular advancement - Bilateral Sagittal Split Osteotomy (BSSO)
or
Maxillary (midface) retrusion - LeFort I Osteotomy
or
Combo surgery - BSSO and a LeFort I
Class III malocclusion (your chin sticks out)
Corrected by:
Mandibular retrusion - BSSO
or
Maxillary (midface) advancement - LeFort I Osteotomy
or
Combo surgery - BSSO and LeFort I Osteotomy
Posterior Crossbite
Corrected by:
SARPE - Surgical Assisted Rapid Palatal Expansion
Often a genioplasty (chin position correction) procedure can be done also with the orthognathic surgeries.
Above is only a general overview, many other options are available depending on your specific diagnosis. All above procedure can be done at an OMFS office or an OR at a Hospital under General Anesthesia. Cost? No idea, probably $2500-$4000 depending on the procedure, I guess.
For more detailed info about the actual procedures, search the internet for:
Lefort I Osteotomy
BSSO
You'll learn much more!
One more thing, many, many orthodontic patients undergo orthognathic surgeries to correct their bite and esthetics so this is not an unusual event! You will be very pleased with the end result, I can assure you. I've always loved Ortho and/or Oral Surgery lectures where they showed Before & After pictures of patients underwent Orthognathic surgeries and what a drastic change in 100% of those patients, especially esthetically!
I can recall many occassions when we saw a case, when there was this female patient underwent orthognathic surgery, her Before photo was lets say below my "taste" and then her After photo was "Hot-o-Mama"!! Wow, what a change!!!
Good luck with your surgery, you're in great hands (literately)!!