I severely sprained my ankle about 20 years ago, leaving me on crutches for about 6 to 8 weeks. What I found that helped me the most was swimming laps. The water acts a natural buoyancy, so gravity is not pulling the blood down into your ankle causing it to swell as it would if you were standing up. Also, as you're swimming through the water, the water acts as a gentle massage on the ankle. I noticed that my ankle always felt much better immediately after swimming laps than at any other time. Just be careful when you kick. If you can kick gently while swimming without it hurting, then fine. Otherwise, just kick with your other leg to keep the lower body afloat while you power through with your upper body.
More importantly, though, make sure your doctor says it's OK for you to swim or do any other exercise.
Hope this helps.