I sprained both ankles, both times from running (note: after that last one I'm hardly running anymore). I did most of the same things that you described (Rest Ice Compression Elevate), went to a podiatrist who did x-rays and gave me a lace-up thing that I wore under a normal (well mostly normal) running shoe.

That last time was my left ankle, the same one I lean on when I stop while riding. While actually riding, I was fine. It was all that stopping...required me to maneuver my foot around to avoid falling. I was fine for short rides (like under 20 miles) for the 2-3 weeks before it was mostly better. As soon as I got home I iced.

Where in Phoenix/Scottsdale are you riding? I live out here... Weather is supposed to be really nice this coming weekend.