I played basketball so I've gotten a ton of sprained ankles.
Dynamic stretching before and after helps a ton, preventatively speaking. Achilles, calf, foot, toes.
Specifically this one thing I do: lay on your back, feet elevated at 90 degrees. Shoes off. Rotate ankle 360 degrees, 5x clockwise/counter clockwise.
Slowly. As much ROM as you can.
Then flex your feet and rotate them up and down. Spread your toes.
Do that 3-5 times.
No more rolled ankles after that (been 2-3 years).
After the injury: RICE it up. Ice, compress, elevate. 20 min each step.
Do this or it will take FOREVER to heal! Ankles get shitty blood flow!
Get a GOOD ankle brace (full straps) and you can run on it. If you're young I recommend aggressive treatment. I ran with a bum ankle for months with a good brace.
Soreness and weakness is fine. Pain is not. Treadmill is low impact too. Massage, even self, helps a ton too. Gl