Could taking antibiotics somehow cause lower back pains or lead to a bladder infection?

Unlikely. Antibiotics are used to treat a bladder infection but if used for long periods of time or high doses it can lead to a loss of normal vaginal bacteria. E.Coli can then start accumulating in the area. Also, the bladder infection itself may be worsening and that can cause increased pelvic, abdominal, and sometimes low back pain.