Orthognathic Surgery is usually done in severe cases of misalignment of jaws. Minor problems can also be corrected braces treatment following extraction of teeth called premolars. Final decision can only be made based on detailed analysis of the severity of the problem. I suggest you to visit any orthodontist nearby for proper assessment and treatment.
Orthodontists are the specialist in teeth straightening. If your jaw bone is not in good shape you may require orthognathic surgery. And if there is problem in teeth alignment , regular braces will work good.
It is good to know the terms like orthognathic surgery, but please don't arrive to such a conclusion and let that be a doctor's decision...... without evaluating the case clinically and examining the xrays, it will be difficult to devise a treatment plan for you..... the main concern that you have mentioned is that you are not able to close your mouth properly most likely that can be even corrected without orthognathic surgery through orthodontic treatment..... please post your clinical pictures as well as 2 X-rays called as OPG and lateral cephalogram.....
Difficulty in closing mouth can be because of many reasons.it is better to get the proper diagnosis by proper investigations then we should come to conclusion about the treatment plan. Generally orthognathic surgery is done in severe cases. My suggestion is to get the X-ray and scan done before getting the treatment.
Dr Vishal Jain