I hate sprains. They take months and months to heal... and if I do too much it just takes even longer.
A sprain SOUNDS better than a broken bone, but it's not. A twisted ankle, sure, that heals fairly quickly. But a break heals soooooo much faster than a sprain.
Absolutely do the physical therapy. At this point, I've sprained my ankles so many times I don't need it, because I know the drill. Wait 2-3 months, then slowly start the exercises that get the tendons and ligaments and muscles back in shape. Too much, too soon just makes everything worse and take even longer to heal.
In general, when I sprain my stupid right ankle, it takes 6 months to be back to "normal". My worst sprain, however, I had to wait 6 months before beginning the PT on it, and it took a whole year to be back at 100%.
Massage can be helpful NOT for the injury, but for the surrounding muscles which get sore, because you're using them more to compensate. Massage on the injury itself, usually makes it worse. My MP is actually a sports medicine person. When I'm injured, she avoids the injury and surrounding area completely... but will work on the opposite leg, and on the unaffected muscles, tendons, and ligaments above the injury.
Go to PT at least once or twice. Explain that that is all that you can do, and they will show you everything that you need to do and give you a timeline and a stack of printouts showing the exercises and when to do them, along with how to know when you've done too much. The hardest exercise to do at home is one of the most important. Strengthening the lateral muscles requires rolling your ankle on a platform with a ball and weights. Oft times I think I'll be fully healed but still have "numb" spots laterally. Until I've reennervated and restrengthened those numb spots using the stupid ball contraption I'm at risk for reinjury.