Did my UTI move to my kidney?

Around 3-4 month ago I wokeup with EXTREME unbearable pain on my right lower stomach it was so painful I couldn't even get up and I was crying. I went to the bathroom and I peed blood I went to the hospital and it was a UTI I got an antibiotic and the doc asked me to visit the hospital ASAP if I still feel pain after taking my antibiotic. I didn't feel any pain afterwards. But 3 days ago I started to feel this stabbing pain on my left back+side and I thought this is my kidney aching because the uti has reached it. Do you think the uti moved to my kidneys? And is it reasonable to think that my side and back hurt because of my kidneys? And shouldn't that med have helped me why did it come back ( if it did) after all of this time? Should I be concerned and go to the doc I wonder if anyone experienced the same thing please share!
Did my UTI move to my kidney?
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