She was getting nervous as the entrance exam approached.
Literal
She [topic-は] entrance-exam [object-を] [in front of-前にして] nervous became.
~を前にして ('with ~ before one, on the eve of ~') is a standard pattern for impending events. 神経質 ('nervous, sensitive') is a な-adjective; ~に+なる is the pattern for adjectival 'become.' ~ていた marks the ongoing past state — she was in a developing nervous state.