Can antibiotics cause weakness or dizziness?

Yes, but it is a sign of a more serious infection than a simple lower UTI. In addition to the typical bladder infection symptoms (pain, cramps, burning, urgency...), symptoms of an upper urinary infection (aka. pyelonephritis or kidney infection) can include dizziness, weakness, malaise, loss of appetite, nausea, vomiting, fever, chills, backache, bloody urine...