。
She shuddered as she thought about the accident.
Literal
She [topic-は] that accident [genitive-の] thing [object-を] thinking [て] shuddered-up.
~のこと ('the matter of, regarding') wraps 事故 to refer to it as a topic of thought rather than the physical event itself. 思って (te-form of 思う) links the thinking to the shuddering — 'thought, and so shuddered.' 震え上がる is a compound verb fusing 震える ('tremble') with the auxiliary 上がる, used here as an intensifier rather than its literal 'rise' sense — meaning 'tremble violently, shudder hard.' The ~上がる intensifier appears in many emotional verbs: 怒り上がる ('become enraged'), 跳び上がる ('leap up'), 燃え上がる ('blaze up').