Upper respiratory tract infection in a 12-year-old is, in the absence of complications, a bedside clinical diagnosis driven by history and examination. The illness is typically viral and resolves on its own, so the value of any imaging is essentially nil.
The guiding principle is appropriateness plus radiation protection in the paediatric age group (ALARA). Imaging is justified only when the picture suggests lower respiratory tract disease — pneumonia, respiratory distress, persistent fever — none of which is stated here. Consequently, the correct next step is to perform no radiological investigation.
Looking at the distractors: a chest radiograph would be the first imaging chosen if pneumonia were suspected; HRCT belongs to interstitial or chronic airway disease workups; and CECT brings contrast plus the highest radiation dose, which is wholly unnecessary for a simple cold.
Therefore no imaging is required.
\[\boxed{\text{No radiological investigation}}\]