A child with fever and sore throat developed acute cervical lymphadenopathy most likely investigation to be done is :
Open biopsy of node
Radical neck dissection
Neck X–ray
Complete hemogram
Cervical lymphadenopathy with signs of infection such as fever and sore throat points towards any infectious etiology.
In this case the most likely investigation to be done should be complete hemogram.
Complete hemogram can provide useful datas for diagnosis of :


Pyogeizic infections.
Viruses such as EBV CMV & HIV.
Leukemias (acute or chronic).

Biopsy should be done if the patients history and physical findings suggest malignancy. These features are :

Solitary, hard non-tender cervical nodes in an older patient.
Neck X-ray does not provide much information except for giving some idea about swollen soft tissues of neck.
Radical neck dissection is absurd option.