。
She couldn't bring herself to say anything emotionally heavy.
Literal
She [topic-は] emotion [subject-が] intense thing [subject-が] could-not-say.
A doubly subject-marked construction. The first が attaches 感情が激しい ('emotions [are] intense') as a relative clause modifying もの ('thing'); the second が is the potential-verb's subject marker, since 言える ('can say') re-marks its semantic object as a subject (Japanese routinely does this with potentials). So the sentence reads: '[the thing] [whose emotions are intense] [could not be said by her]' — i.e., she couldn't bring herself to say emotionally charged things. This kind of nested は…が…が structure is one of the hardest features of Japanese to read at speed, but it's how the language packs information cleanly without subordinate clauses or relative pronouns.