CT scan for stones — with or without contrast?

Hey everyone, first time dealing with a possible stone back in January. I didn't even know what stone symptoms were until after the fact. I actually turned down the CT because of the contrast dye. What are the alternatives? My urologist seems convinced it's the only option. I'm pretty sensitive to medications so the idea of getting injected with contrast makes me nervous.

Backstory: In January I had what I assumed was a back strain even though I never did anything to cause it. It came on super sudden, really severe, couldn't move without pain, plus cramping and pain radiating from my back around to my stomach. Turns out those could've been stone symptoms. I've also had microscopic blood in my urine that they're trying to track down. Has anyone had a similar experience? What was your RBC count? Did you have symptoms like mine? I had a baby two years ago and had been writing off dull back pain as just normal postpartum back stuff. Once that possible stone passed in January my back pain just magically disappeared. But I still have blood in my urine so now they want to do the imaging study and a cystoscopy.