Final answer:
Oliguria is the most urgent finding a nurse should report to the provider when a client is on tobramycin, due to the risk of nephrotoxicity and kidney impairment.
Step-by-step explanation:
A nurse who is collecting data from a client taking tobramycin should report certain findings to the provider immediately. Of the options provided, oliguria, which is the production of abnormally small amounts of urine, should be reported to the provider as soon as possible. Tobramycin is an aminoglycoside antibiotic that can cause nephrotoxicity, potentially leading to acute kidney injury. Oliguria can be an early sign of kidney impairment due to the nephrotoxic effects of the drug, so it is important for it to be assessed and managed promptly to prevent further damage to the kidneys. While reports of nausea, fever, and headaches are also concerning and should be addressed, they are not as immediately alarming in the context of tobramycin therapy as oliguria, which could indicate a serious adverse reaction to the medication.