If the burning is prostatitis, the bounce is linked. If the burning is bladder or urethra related, the two issues are coincidental and not linked.
As I mentioned before, PSA bounces may occur when the cancer cells "explode" releasing their PSA. Healthy tissues slough off as well, releasing their PSA. Eventually, the cancer cells will self-destruct and the healthy cells will stay healthy and the PSA will go down.
I realize you had a lot of radiation with the IMRT on top of the seeds and that's bound to irritate the tissues. What are you taking for it? Some guys I know swear by Elmiron.
It sounds like if you take a PSA test now and it is still bouncing, you will worry about
it. And if you avoid your scheduled PSA test, you will worry about
it anyway. So if either decision will cause you to worry, the decision doesn't make a difference. I think your best bet is to acknowledge that you had definitive treatment, and the PSA will go down in its own good time. You have not met any of the criteria for biochemical failure. One can only deal with things as they are.