From the symptoms and the exact nature of the problem that you have mentioned, it can be ascertained that the problem you are facing is Achilles tendonitis. This condition is an inflammation of the tendons of the ankle and is not a serious condition to worry about if proper care and rest is taken.
The tendons are a very important part of movement in the body. To understand the strength and power of the tendon, you can find an equivalent in sinew that is obtained from animals. Tendons are basically a high concentration of collagen fibers. Curiously, collagen is also in an important part of the skin. Collagen is a tough long stranded fibrous protein, biochemically speaking. The function of a tendon in the human body is to connect the muscles to the bones. As a field of reference, ligaments connect bone to bone, and fascia connects muscles to muscles. Muscles and tendons have to work together by pulling and relaxing for movement to occur. Tendons are almost elastic in nature and have the ability to store energy when taut just like an elastic band. However, as you have just experienced, tendons are not made of steel and are also subject to injury. Achilles tendonitis is the inflammation of the Achilles tendon, which is caused a sudden stretch that ripped the tendon. This is a minor injury but if not treated properly and immediately, can cause perforation and tendonosis, which is the chronic form of tendonitis that is much more difficult to correct. Regular medical treatment for this condition involves resting the tendon completely - the point of even getting the entire limb in a cast to avoid movement. While this might be an extreme case, it highlights the importance of ensuring the tendon needs rest. Apart from this, non-steroid anti-inflammatory drugs or NSAIDs are administered along with a cold compress therapy. Cold compress is useful to reduce swelling in the area. In a span of three days, this should take away the constant pain and then the tendon has to be slowly nursed back into making regular movements and not forced right away and this is why a complete recovery from this condition takes almost six weeks.
As a home remedy, increase your dietary intake of antioxidants and consume anti-inflammatory herbs like ginger and frankincense resin to reduce the inflammation. In the tender period, you should also keep your foot raised above the level of your head and not move the ankle at all.