This unsteady feeling in your ankle may start to improve once the swelling and pain subside. Swelling can put pressure on the nerve sensors that are responsible for your sense of joint position. Also, pain can keep muscles from doing their job of protecting the joint. The effects of swelling and pain may combine to make your ankle feel unstable.
However, it is possible the ankle could feel unsteady even after the swelling and pain have gone away. This usually involves injury of the nerve sensors. The injury can be caused either by the trauma of the sprain itself or the pressure from the swelling.
You may need to do special training exercises, called proprioception exercises, to improve the joint's stability. These types of exercises are a lot like doing balance training. Examples include balancing on one leg with your eyes open and then closed, walking on uneven or soft surfaces, and practicing on a special balance board. If your ankle keeps feeling unsteady, you may need the help of a physical therapist who will design a program that will probably include these types of exercises.