、。
Kyoko, startled by the thunder, came clinging to me.
Literal
Thunder [by-に] was-startled Kyoko [subject-が], me [to-に] clung-came.
雷に驚いた is a relative clause (thunder-startled) pre-modifying 京子 — Japanese piles modifiers in front of the noun, where English usually needs a comma clause or a 'who' relative. に marks the source of the startling. しがみついてきた pairs the main verb 'cling' with the auxiliary ~てくる, which physicalizes the motion toward the speaker — she didn't just cling, she came clinging. A core Japanese trick: the direction of an action is baked into the verb phrase, not a separate preposition.