。
She clung tightly to my hand.
Literal
She [topic-は] my hand [to-に] firmly clung.
しがみつく is a vivid verb conveying desperate clinging — a child to a parent, a survivor to a rope, someone overwhelmed by emotion to another person. The に here marks the point of attachment (the hand being clung to), not direction or recipient. しっかり (firmly) is a 擬態語 (state mimetic) capturing solidity or steadiness — pair it with verbs of holding (しがみつく, つかむ, 握る) and it adds the sense of 'with full force, not letting go.' The kanji 付 in しがみ付いた is unusual; しがみつく is more commonly written all in kana.