Can UTI cause like period cramps under the bowel? In urine I noticed white pieces. When I pee it doesn't burn.

Possibly. Typical symptoms of UTI include all or sometimes just a few of the following: urinary urgency, frequency, voiding small amounts, burning, bladder pressure or discomfort, and cloudy and malodorous urine. Some women, especially older woman, may have asymptomatic bacteriuria: no symptoms other than maybe cloudy urine. Sediment in urine may be infectious or not. Urinalysis and culture recommended.
Possible stones. Kidney or bladder stones can cause intermittent blockage and be associated with cramps and pain. It is possible that the "white pieces" are indeed fragments or sediment of calcium, especially if you do not have burning, more indicative of infection. See your family doctor, save a urine specimen (or give one when you see your md) to check.