Severe lower back pain radiating through sides and sides of belly. Blood in urine early today. Period ended 2 days ago. What could this be?

Infection or stone. You likely have a kidney stone, though a urinary tract infection can cause similar symptoms, especially if tracking up from the bladder to the kidney(s). I think you should see your doctor for further evaluation.
Here are some ... Although the pain you described is not typical for something like stone or clot passing through ureter (a tube transporting urine from kidney to bladder), seeing gross bloody urine is the concern especially if no UTI (cystitis) is found. So, nonetheless, see Doc to figure out both common concerns for one in a 21-yr female. Of course, bring the info on the onset, degree, duration, & progress to Doc.

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