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I understand your concern. So you have had kidney stones before. While a patient has UTI and if it's not controlled there can be lower back pain and a " fever " feeling throughout. I need to know whether the doctor did any urine culture on you before diagnosing you with UTI. Normally we do urine culture straight away, because some antibiotics are resistant and we need to find which antibiotic is sensitive to the organism.
What medicines are you currently taking? Also how high is your fever? To control your fever you can just rely on the OTC Paracetamol, which can be taken twice daily after food ( minimum 8 hours duration ) and that will reduce your back pain too.
You can discuss with your GP regarding the matter, and take a course of Tab. Nitrofurantoin for 7 days thrice daily after food. Most bacterias are sensitive to Nitrofurantoin. Also make sure you drink a lot of water or consume a lot of fluids to prevent your urine from turning acidic which might be causing the burning feeling during urination.
In case your pain doesn't subside in a day or two, you can get an USG WHOLE ABDOMEN done. It will give us a better picture.