Last time I sprained my ankle to a point that it swelled up and bruised I was out for a long time. Happened two years ago, and it still aches some times. I have a high pain threshold too, so when I say it aches, it REALLY hurts.
Sprains are like breaks and burns; Many different degrees which make a big difference on healing times.
1st Degree will heal in no time, and by the next couple days should be ok. basically just stretching the ligaments.
2nd Degree takes awhile longer, you have actually damaged some of the ligaments, might be some bruising (ligaments bleeding)
3rd Degree is where you have completely ripped some or all of the ligaments, bruising on both sides can happen, massive swelling, and might need surgery to repair.
When I did my 3rd degree is was far worse than any broken bones I've ever done, and actually take much much longer to heal. Not pleasant at all.
If you can get a prescription, and have coverage, go to rehab. I didn't bother cus I was too busy with work, and I definitely regret it.