Hey there... sorry, I guess I didn't see your post, or I'd have responded.
What you're describing could be a number of things (UTI, bladder-infection, renal-lesion, kidney-stone), but as you have a history of kidney-stone formation, I'd tend to lean in that direction.
When a kidney-stone hits the wall of the kidney, it sometimes will 'know tissue loose', and when you urinate, it'll be included in your urination.