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Your injury could well be totally different to mine but for what its worth:
From memory there was a period of months with no cycling or running while I concentrated on light stretching and eccentric exercises. When I began to sense an improvement I think I spent about two months building up my walking until I could walk for 90 minutes, up and down stairs with no pain or creaking. I think that's the point I was allowed to start doing calf raises and start a very gradual return to running...basically a couch to 5k followed by a progression to 10k over 7 months while carrying on the achilles exercises. That's a high level really.
Nothing will beat finding a good physio and working with them as if your achilles depend on it.
Did you go from nothing to 13km over two months? My gut feeling says that's quite fast depending on how bad your tendonitis is/was and how long you rested for.
I had moderate tendonitis in both achilles in 2011 and it took me about 7 months to build up to 10km under physio supervision. Different injury I know but it took me a year to safely build up to 10km after an ACL tear. Achilles are slooooow to rehab.
I can recommemd a very good physio based in Greenwich. They were recommended to me by an army knee surgeon and have seen me right through two nasty injuries. PM if useful to you.