That said, I must also say that I do not believe you can damage your feet from wearing good, supportive shoes. I believe you have already damaged your feet if (like me) your wore cheaper shoes and didn't pay attention to the pain the very second it started.
Birks may not be for you. There are certainly other excellent shoes to try and they are mentioned all over this board and Scott's main site. The point is, while good shoes help, you can probably expect to have continuing pain for awhile. I started with Birks last December or January and got almost immediate (partial) relief. But not complete relief by any means. It has taken (and continues to take) numerous other steps for me, such as diet changes, supplements and exercise. My suspicion is that you are feeling pain in your heels with Birks because of the lift to the fascia tissue itself with the Birkenstock arch. I would give them a reasonable amount of time (a couple of weeks anyway) and consider trying additional brands if they(Birks) don't work pretty well for you.