Step 1: Start with the plain film. No calcific density anywhere along the tract removes a calculus from contention from the outset.
Step 2: Move to the contrast study. The distal left ureter balloons into a bulbous opacity that looks like a snake's head, ringed by a thin lucent rim - the classic cobra-head plus radiolucent-halo combination. This pattern is pathognomonic of a ureterocele protruding into the bladder.
Step 3: Understand the lesion: a ureterocele is a cystic out-pouching of the terminal ureter. It is commoner in females, accompanies ureteric duplication in roughly three-quarters of cases, and the pooled, stagnant urine inside it seeds repeated infections - matching this patient's recurrent UTIs.
Step 4: Exclude the rest: simple ureteric duplication lacks the terminal sac, a congenital megaureter widens the ureter along its length rather than forming a discrete head, and stones are already ruled out by the clean plain film.
\[\boxed{\text{Ureterocele}}\]