You are fortunate that your doctor recognized the true nature of the problem early on. Syndesmosis injuries are often missed during the acute phase. This can lead to many problems later on.
The syndesmosis is made up of several soft tissue structures in the ankle. The first is the interosseus membrane. This sheet of connective tissue holds the two lower leg bones together. The second is a set of ligaments between the two bones. These are called the tibiofibular ligaments. There are three segments to the ligament: anterior, inferior, and posterior. They are named for the location (front and back; top and bottom).
It's a well-known fact that syndesmosis ankle injuries often take longer to heal than other ankle sprains. The lack of ligamentous support for the bones of the ankle transfers a tremendous amount of force directly to the bones rather than up the leg to the knee.
The physician usually diagnoses the type of injury as grade I, II, or III. Surgery may be needed for grade III. The bones are pinned together and the patient is put in a non-wearing boot for six weeks. At 12 weeks the screws are removed and the patient is allowed to start putting weight on the foot. There may be some rehab needed to restore strength and proprioception. Proprioception is the joint position sense needed to make cuts and quick moves.