Achilles tendon injuries are one of the more common running injuries. They can occur in any runner, but they are more likely to occur in those who are just recently starting to run again, or ramping up their training intensity. For example, if you are just recently pushing yourself to run at higher speeds, that might be the cause.
You are also right that another risk factor for achilles tendon injuries is increasing age. The older you are, the more fragile the tendon is and the slower it will heal. In fact, most achilles tendon injuries do occur in middle-aged runners.
If you are having pain or discomfort in your achilles tendon, it is imperative that you back of your training regimen and rest. Achillles tendonitis must be allowed to heal because, if not, continuing to run on an inflammed tendon puts you at high risk of a tendon rupture, which is a very serious complication.
In addition to rest, icing the inflamed area and taking anti inflammatory medications like ibuprofen should help with the pain.
I suggest that you also go see your primary care doctor
to make sure there is no evidence of serious tendon injury