I have battled Achilles tendon issues for years, including retrocalcaneal bursitis. It sounds like you’re case is relatively new and may be more easily fixed than mine was. One thing you might try, and that helped me for some time, is eccentric lowering exercises. These are very effective for Achilles tendon issues… particularly when they are in the body of the tendon, but also for insertional issues if done correctly. They are done by rising up on the balls of both feet then lowering down, slowly, on just the affected foot. (If both feet are affected do both… rise up on 2, lower slowly on 1.) The main difference for insertional issues is that you only lower your heel to a flat floor rather than standing on a step and lowering your heel below the step as for issues in the main body of the tendon. These are exercises a physical therapist could help you with.
Another thing you might check on is the presence of a Haglund’s deformity (identified by an x-ray). If this is present, you may have ongoing issues (as I did). If you have a Haglund’s deformity and months of PT/rest don’t help, and can provide additional advice.