She looked around her.

Literal

She [topic-は] herself [possessive-の] surroundings [object-を] looked-around.

自身 (じしん) is a slightly more emphatic reflexive than 自分, often used to underscore 'oneself in person' or 'one's own.' Here 自身の辺り means 'around herself, her immediate surroundings.' 見回す ('to look around, to survey') is a compound verb (見る + 回す, 'look + spin/turn') describing a sweeping visual survey. Note the slight redundancy — 彼女 is the subject and 自身 echoes it; this is normal usage and emphasizes that the surroundings are hers specifically rather than someone else's.