The pain is usually felt more to the inside of the tendon. >>Pic 1 Mid tendon<<. Tendons as sore to poke so compare with the other leg to see if you have found the right part. There may be a spot of thicker fibrous tissue.
These types of Achilles issues can be due to tearing or over-loading of the tendon. If it is only a few days old then please rest and ice. If it is longer than a couple of weeks then start to work the strength of the calf and Achilles with heel rises or eccentric lowers. Eccentric lowers have been in favour recently due to some good research.