Ice and anti-inflammatories are your short-term friends when your Achilles tendon is inflamed. The anti-inflammatories are especially helpful because blood flow to the tendon is limited, so it can be tough to get relief solely with icing. While you have Achilles tendinitis, put a slight heel lift in your non-running shoes to take some of the pressure off the tendon; corrugated cardboard, swapped a couple of times a day once it starts to compress, works well.
Same deal here as with plantar fasciitis: Getting Achilles tendinitis usually means you need to improve range of motion in the tendon and your calves. Part of that is not wearing heeled shoes during your non-running hours. In your running shoes, be sure the heel counter doesn’t rub your Achilles tendon.