I sprained my ankle in December of 2010 and the pain didn't subside because I skied on it through April.
Worst season, but I didn't want to take time off to let it heal.
Best medicine is to let it heal, but let's be realistic. On the flipside, don't take SHIT from people calling you a pussy. Clearly they've never had a bad sprained ankle. My ankle forever pops now when I hike or run.
Hears the deal, LEARN TO TAPE YOUR ANKLE.
Roll of athletic tape and a roll of pre-wrap goes for about 2-3 bucks. Tape it before you ski. It's not too difficult, just make sure to buy the pre-wrap because peeling athletic tape of your leg SUCKS. It rips your skin and your hair.
Stock up and get about 5 rolls of athletic tape. Usually take about 70% of a roll to tape your ankle.
It'll keep your foot from moving and help stabilize your ankle in your boots. With a properly taped ankle, you can run on it with little to no pain.
Her's the video tutorial I learned from (that and having a friend practicing sports medicine was huge):
As others have said, practice the RICE method. Rest, Ice, Compress, and Elevate.
At night prop your foot up with a pillow so it's above your heart. This will help to reduce the swelling.
Take an anti-inflammatory like Advil or Tylenol about 1-2 a day (400-600mg each time) or as needed (days of skiing I usually took 800mg in the morning when I woke up and 600mg around 1). That's a lot of advil, but I never take it and I'm a decently sized athletic guy so it was fine. Just make sure not to drink while taking that much anti-inflammatories.
Purchase an ankle brace, or an ace bandage. When walking around town or class, wrap it with an ace bandage or use the ankle brace. It will help to reduce movement and promote faster healing.
Lastly, ice on 15 minutes, ice off 15 minutes. Do this three times twice a day.
DO NOT USE HEAT UNTIL THE THIRD DAY. Heating too early in the healing process can damage ligaments. Likewise, icing too long will damage ligaments. Make sure to stick to 15 on and 15 off 3 times with at least a 4 hour break in between sessions.
I am no doctor, but I had sustained a Type II ankle sprain and know a SHIT ton about sports medicine that goes along with it.
Best of luck man. Skiing with a sprain SUCKS DICK, but it can be done. Just don't go as big while it heals.