The type of sprain you are describing is called an inversion injury. It’s likely that you sprained a ligament inside the joint, not the muscle around the ankle. Ligaments can’t be strengthened with exercises. Instead, the muscles around the ankle are improved. In this way, the muscles can help protect the weakened joint.
Ankle rehab does include muscle strengthening, along with other exercises, as well. Stretching to keep flexible and exercises to help the joint sense what position it’s in are important parts of the program. In the past, exercises focused on muscles along the outside of the lower leg.
A new study by physical therapists in Australia has challenged this method. They found that weakness of the muscles along the inside of the ankle (called invertors) is the real problem. Exercises after an inversion ankle sprain should focus on the invertors.