Yes, keep taking your meds and see your doctor often.

You should have a renal sonogram. Back pain can be caused by renal stone, obstructive uropathy, and pylonephritis.

Yes, kidney infections or bladder infections can cause side pain or back pain. I would also recommend a kidney ultrasound to make sure you don't have kidney stones.

Usually, kidney infection (pydlonephritis) causes flank pain along with other symptoms like fever, nausea, vomiting, and urinary symptoms. Unlikely to cause back pain as a sequel. If you had a severe kidney infection with bacteremia and later developed back pain, then it may be worth considering a disc (vertebral) infection as the etiology of the back pain. Or you may have a back pain not related to the current infection at all. It is better to inform your situation to your nephrologist or PCP.
Hope this will help you.

Kidney infection can cause back pain