To add on to the above advice....
Do not mess around with achilles pain. If you snap your achilles, you have to have surgery to reattach, rehab is 6 months, and you'll never run like you did before. Not a light matter...
Achilles issues usually stem from chronically tight calves. That being said- Stretching (as helo wifey mentioned above) is key, lots of easy stretching. Also, ask a trainer or massage therapist about "foam rolling" or look it up online. Essentially, you can purchase a foam roller for about 10-20 bucks and use it to release "knots" in your calf muscles through myofasical release. I could go on, but googling it would save everyone here from boredom. As a person with calf issues, the foam roller is jesus to my running program. Also, make sure you're not pushing it with your runs- no unstable surfaces (like the beach). Run on dirt paths if you must, otherwise take a break for a while and ease back into things. Also, massage is an awesome way to get your calf muscles back in shape.
Don't take the pain lightly and "push" through it unless you'd like to push back your OCS date as well.