I would say definitly you should see a Urololgist. They will probably do a cystoscopy to get a look at your bladder. Hope you get answers. As an IC pt. I know that bladder problems are no fun.
A urine sample submitted for a microscopic examination should tell what it is. A cytologic examination would also be a helpful test. Inflammatory conditions (IC) and infections of the bladder wall can cause sluffing of the lining and produce a lot of cellular material and debris, however a bladder tumor can shed cells and tissue as well. Start with the urinalysis, culture and cytology thru your primary care doctor and go from there. Good Luck.