With a short chin associated with lip strain, the best procedure is a sliding genioplasty because it moves the bone and the attached mentalis muscle. This corrects the anatomic basis for both problems.
Recurrent swelling and resolution with antibiotics leads me to believe that you might have a low grade infection of the implant. Please see your plastic surgeon as soon as possible for an evaluation and recommendations.
Everyone has some degree of facial asymmetry. You do have some asymmetry which can be treated. You have a smaller jaw (mandibular angle) on one side which can be enhanced with Radiesse for a quick, easy treatment. You would also benefit from filler to the chin or a chin implant...
