I have a sore achilles tendon from running. do i risk serious injury if i keep running? is rest the best treatment? for how long?

Yes: If at is hurting rest it. Listen to you body when having pain. However, don't listen to your Achilles when not hurting. Meaning, when returning to running go gradually: do rest, tylenol, (acetaminophen) masssage, may be pt then do graudal return to activity-> walk, then faster walk, short jogging (on grass, threadmill), then run and advance distant and intensity carefully.. Do proper warm up, streach, & rest.

Yes: You could cause serious injury including tearing of the tendon. Rest is a good thing. I would see a doctor for further care.