use get_page_by_title to get post by title.
I check for it on my system
$post_exist=get_page_by_title( 'Hello world!', ARRAY_A, 'post' );
if( ! empty( $post_exist ) ) {
echo 'title exist';
} else {
echo 'title not exist';
}
Running successfully.
In your case it may be like
$title=trim($titles_arr[$i]);
$post_exist=get_page_by_title( $title, ARRAY_A, 'post' );
if( ! empty( $post_exist ) ) {
echo 'title exist';
} else {
echo 'title not exist';
}