I respect that this is a water only fasting forum, but your main inquiry is about healing your sprain so I will keep it brief.
Nothing heals inflammation faster and better than urine in my opinion. Bathe it for 5 mins as often as you can. I believe ice as mentioned should not be ignored.
If you drink a glass of urine the pain and swelling will reduce very markedly within about 15 mins. You will be limping on it shortly. Keep it up at least once a day and you will be walking on it in a day or two.
If you do a urine fast it will dramatically accelerate the process.