Final answer:
Perform a lumbar puncture to assess cerebrospinal fluid and initiate antibiotic therapy if meningitis is diagnosed.
Step-by-step explanation:
The most appropriate action for a nurse assessing a young child who is febrile and appears ill, with hyperextension of the child's head (opisthotonos) and pain on flexion, would be to perform a lumbar puncture to assess cerebrospinal fluid (CSF).
Meningitis, an infection of the tissue surrounding the brain and spinal cord, can present with these symptoms. A lumbar puncture is the primary test for meningitis, where a needle is inserted into the spinal canal to collect a sample of CSF for analysis. If meningitis is diagnosed, antibiotic therapy would be initiated to treat the infection.