I don't know what a PET scan is, the only insight I might add is I have read hundreds of posts on this board and I don't recall every reading one about a PET scan. So, it must not be very commonly done, but my memory isn't the best, it may have been discussed here many times, do a search that'll give the history.
That said, I read that your doctor has not been able to rule out blockage in the heart muscles, to my knowledge the key reason for running a stress even a nuclear stress test. If these test indicate a problem, as they have in my case - false positive - one goes for a heart catheter examination. That is invasive, and while very safe is more risky than non-invasive tests like echo/ekg/stress.
A problem in the USA health system, is doctors over prescribe (assuming insurance or other ability to pay) tests to protect themselves if a malpractice law suit should occur. I say this from what I read in the "press", I don't think my doctors have done unnecessary tests, but then I do have heart problems.
Here is my result from a search on PET: