Achilles tendinitis is a frustrating condition that can take a long time to heal. You don’t say how long you’ve been experiencing symptoms; according to the American Academy of Orthopaedic Surgeons, this condition can take over 3 months to heal, even with early treatment.
It sounds like you’re doing everything you can to reduce inflammation; biking is non-weight-bearing, and your commute is short — so I wouldn’t expect that to aggravate your Achilles tendons. If you experience discomfort with biking, put that on hold until you feel better; swimming might have to be your exercise of choice until your symptoms resolve.
I urge you to talk to your health care provider as soon as possible for a complete evaluation of your symptoms. Additional tests and treatments may be warranted to identify the source of your pain, provide relief, and help you heal. Unfortunately, there aren’t any short cuts to a complete recovery; be patient, and keep up the good work with your home care plan. Check out the link below for more details on this perplexing condition.