You're on the right track by using ice and a wrap for your ankle. Rest, ice, compression, and elevation--known as the RICE method--can reduce pain and swelling in your ankle and help get you back up to speed.

Your coach has a point, too. Research suggests that physical therapy helps ankle sprains heal faster than RICE alone. In a recent study, patients who had physical therapy had less pain and more ankle movement than patients who only had RICE. The therapy these patients received included specialized hands-on movement of the ankle joint. This technique, known as joint mobilization, may speed healing by improving movement in the ankle. 

Fortunately, the body has natural healing mechanisms, and your ankle will probably heal eventually, with or without help. But if you're serious about getting back on the track faster, guided treatment with a physical therapist is your best bet.