I had tendonitis in my left lower arm for well over 6 months.
Doc said rest (but keep mobilising gently) and take ibuprofen maximum strength every day. I did this for a couple of weeks before getting bored the first couple of times, but eventually stuck with it and after about a month, it did seem to help. Eventually fell out of the habit of the pain killers when it didn't hurt so much and it's continued to improve, but it took a Very Long Time.
Gentle stretching did seem to help, as did icing regularly.
I certainly wouldn't run on an achilles with tendonitis, that seems a really good way of upsetting it to me, but IAMNAD (though I was a nurse for a while).