You mentioned that you underwent surgery a month ago for the mandible fracture
and the swelling still persists. I would also like to know that at the time of procedure any of your tooth/teeth were also extracted/removed?
The reason of the swelling may "NOT" be only due to the fractured mandible, swelling may be due to the following reasons also:
*Incomplete healing, you may wait for few more days
*Improper reduction of the fractured segments
*and at last and most important of all is some tooth may have become non-vital/dead due to which swelling may develop. So the tooth lying in the fracture line is mandatory to remove.
Apart from the fracture line the tooth/teeth which also sustained heavy blow may also become dead and may cause swelling.
Your jaw might be immobilized by wires, you may seek a dentist
after it gets opened.
Hope it works for you. You may mail me pic of your OPG/X-ray for further opinion.