Cervical Strain or Sprain: Given the mechanism of injury, where the patient was lifted by the neck over the seat, and the symptoms of pain to the chin, throat, neck, and upper chest, especially with pain on movement, a cervical strain or sprain is the most plausible diagnosis. The absence of severe respiratory distress or difficulty swallowing also supports this diagnosis.

Cervical Contusion or Bruising: The redness noted to the neck could indicate bruising or contusion from the impact, which is consistent with the mechanism of injury and the symptoms presented.
Mild Thoracic or Chest Wall Injury: The pain to the upper chest could suggest a mild thoracic or chest wall injury, such as a contusion or strain, from the force of being lifted and thrown into the back of the gator.

Cervical Spine Fracture or Dislocation: Although less likely given the low speed and the patient's current lack of severe symptoms, a cervical spine fracture or dislocation is a potentially deadly condition that must be considered, especially with any mechanism involving significant force to the neck.
Tracheal or Laryngeal Injury: The initial difficulty breathing and pain in the throat with neck or head movement could, in rare cases, indicate a tracheal or laryngeal injury, which is a medical emergency.
Pneumothorax or Hemothorax: Despite the current lack of respiratory distress, the mechanism of injury could potentially have caused a pneumothorax or hemothorax, which might not always present with immediate severe symptoms.

Spinal Cord Injury Without Radiographic Abnormality (SCIWORA): This is a rare condition where spinal cord injury occurs without evidence of fracture or dislocation on imaging. It's more common in children due to the greater flexibility of their spines.
Vascular Injury (e.g., Carotid or Vertebral Artery Dissection): Although rare, the force of the injury could potentially cause a vascular injury, such as a dissection of the carotid or vertebral arteries, which would be a serious and potentially life-threatening condition.