I had the injection into the Bursa and it worked immediately tho i didn't run for 3 days. It felt great to run pain free but ....... it only masks the problem and does not cure it. After 6 months the pain gradually returned, i waited for about a year and had a second injection, this one lasted 3 months. I decided no more as i read that too much corticosteroid will eventually weaken the tendon and it has with me. Would i recommend it, I'm afraid not.
If you do go down the injection route, the injection has to be administered in exactly the right place so make sure its someone who knows what they are doing.
Good luck with what you decide on and your recovery.
You might find the following i/view helpful with Hakan Alfredson, a runner and well respected person in this field. If your Achilles pain is where it attaches to the heel bone then be careful it does not develop into Haglunds Deformity which can be a result of pain in this area. Hope you recover soon.
2011 took my running in a new direction as i entered the world of ultras and loved it! Finished my first 100m NDW in 24.53 so my target is to go under 24hr this year, also to finish the Zegama-Aizkorri marathon in the sky running series which is the only race i have failed to finish in 32yrs of running - its tough !!. I will also enter SDW and if i fail to get a UTMB place the NDW.