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She screams just from someone touching the bone in her elbow.
Literal
She [topic-は] elbow-tip [of-の] bone [in-に] is-touched [just by-だけで] scream [object-を] raises.
肘 ('elbow') is written here in katakana ヒジ — a stylistic choice that makes a body-part word jump off the page, common in casual writing and in contexts emphasizing the physical sensation. ヒジ先 refers to the very tip or point of the elbow — the bony prominence that would scream-worthy on contact. The passive 触られる takes に for the agent slot (here unstated) and combines with だけで to give 'just by being touched.' 悲鳴をあげる ('let out a scream') is a fixed light-verb expression where 悲鳴 ('scream of distress') becomes the object of あげる ('raise, lift, emit'). The phrase covers anything from a yelp of pain to a horror-movie scream.