KO. I had an achilles injury, and it took 18 months to overcome. I tried all sorts icing, physio, rest etc. Sure I ran during this period but after a few weeks I would break down again. It turned out I was pronating, so that every time I ran the tendon was twisting and was unable to recover. Got myself some orthosesis, and have never loked back.
My advice is rest. Coz of poor blood supply phsio doesn't really work. Once you have no pain in the morning, wait another week. Then try running. If everything is ok, fine you've got away with it. Just remember in future any pain from the achilles stop running immediately. If the pain returns within a few weeks, you've got a much more serious problem. You have to find the underlying cause. Go and get your running gait analysed.