Yesterday we had lunch with my endurance-sports-mad doctor and sister-in-law, so I took the opportunity to get the good oil about icing Achilles (or any tendon strain). What she said made sense: the early application of ice is important as it reduces the inflammation. The combination of both ice and ibuprofen reduces it even more effectively. Resting helps even further again. Thereafter recovery and treatment depends on the type and extent of the injury.
An actual tear or snapping of the tendon requires different and specialist treatment of course, but simple inflammations can be treated effectively with ice in the first 24 hours to reduce the swelling, and rest thereafter. It will still take time to heal, but reducing that early swelling will help a lot.
Now of course the obvious question, which I totally failed to think to ask at the time, is "so why does the body cause swelling around an injury in the first place?" My brief research on the topic seems to say that swelling is the body's way of protecting the injured area from infection. The pain the swelling causes also slows us down, thus preventing any exacerbation of the injury. The problem with all this is that it interferes with the blood flow to the injured area and whilst protective, it does slow down the rate of healing. Or so the theory goes. In this day and age the need to protect an injury from infection is greatly reduced; ergo, reducing swelling actually speeds the recovery process.
Neat, huh?