Read the trajectory of this illness. A toddler has been running a purulent nose for a while, now spikes a fever, and develops a red, swollen, puffy eye while x rays light up the ethmoid sinus. The ethmoid air cells sit right against the medial wall of the orbit, separated only by a paper thin bone, so an ethmoid infection that pushes into the eye is the textbook setup for orbital cellulitis or a subperiosteal abscess.
The management hinge is anatomical. Is the swelling stuck in front of the orbital septum, or has pus tracked behind it into the orbit and possibly walled off as an abscess? You cannot answer that by looking at the eyelid alone, and a postseptal abscess may need urgent drainage.
That is exactly what a contrast $CT$ of the orbit and sinuses delivers. It maps the sinus disease, distinguishes preseptal from orbital extension, and reveals any collection that the surgeon must evacuate, so it is the logical immediate next step.
The alternatives fall short. A urine culture is irrelevant to a sinus and orbit problem. A blood culture is reasonable supportive testing but is often sterile in a focal orbital infection and tells you nothing about whether an abscess exists. Repeating the conjunctival swab is pointless when the first grew nothing and the real pathology lies deep behind the eye, not on its surface.
\[\boxed{\text{CT scan}}\]