what does "secured space for second thought" mean?

It means that by resisting her first impulse to scream, she gave herself the opportunity to reconsider the event (to secure space for second thought), which lead her to decide to tell no one. "Second thought" is a common expression in English which means to reconsider, to review or judge a person, an event or a circumstance again more carefully than is the case in the initial reaction.

She / secured / space
for / thought

secured space = set aside time