She was so embarrassed that she couldn't say anything.
Literal
She [topic-は] extremely embarrassing thought [object-を] was-made-to-do [then-て] nothing couldn't-say.
恥ずかしい思いをさせられて combines causative (させる) and passive (られる) — she was *made to feel* embarrassed by someone. The causative-passive is one of Japanese's most complex constructions.