。
She couldn't help worrying about her son.
Literal
She [topic-は] son [genitive-の] thing [object-を] worry-without could-not-be.
~ずにはいられない ('cannot help but / cannot keep from') is a literary/formal pattern combining the classical negative ~ず, the contrastive には, and いられない ('cannot be / cannot exist'). Literally 'cannot exist without doing X' = 'cannot help but X.' Past form ~ずにはいられなかった narrates a sustained inability to refrain. 心配せず is the classical-style negative te-form of 心配する, fitting the formal pattern's flavor.