Is it possible that my misaligned bite is also giving me sleep apnea?

It's possible: When considering anatomic factors that may predispose a person to having sleep apnea, the position of the mandible (jaw bone) may be important. Since the tongue is attached to the mandible, a receded chin will put the tongue in a retruded postion (toward the back of the throat) which decreases the space in the throat for breathing. This is further exacerbated by sleeping supine (on back).

Apnea: Obstructive sleep apnea (osa): osa is the most common form of sleep apnea. Obstructive sleep apnea occurs when the airway is blocked or obstructed during sleep. This can be caused by tissues in the through such as the tonsils or adenoids, by the tongue blocking the throat, or by other contributing factors, such as sleeping position, obesity, or genetics. Allergies and illness have also been known.