Final answer:
Oliguria should be reported immediately to the provider, as it is a potential indicator of acute kidney injury from tobramycin use.
Step-by-step explanation:
Among the symptoms provided by a client taking tobramycin, the nurse should report oliguria to the provider immediately. Oliguria, which is a significant decrease in urine output, can be an indicator of acute kidney injury, a known side effect of aminoglycosides such as tobramycin. This symptom requires prompt attention to prevent further renal damage and to assess the need for a possible change in therapy. While nausea, fever, and headache are also important symptoms, they are not as immediately concerning as oliguria in the context of tobramycin use which may reflect nephrotoxicity.