Kidney stone ?

Can a ct scan possibly miss a kidney stone ? So I’ve been having symptoms of a uti constant peeing & feeling like I have to go and struggling to push also had some occult blood and proteine in Urine second round on macrobid but I also get nauseas and cramping around pelvic area and back pain I did feel like I have to push a few days ago like a minor contraction and it went away I did notice I had little brown specs in urine not blood or brown urine my doctor recommended I get another ct scan but what do you guys think I hate having to go get another one due to radiation