If paragraphs in your text file are consistently separated by one or more blank lines, setting $/ to an empty string will allow you to read the file in "paragraph mode" -- i.e. one paragraph at a time:

open( IN, $file );
{
    local $/ = "";
    while (<IN>) {  # $_ contains a paragraph of one or more lines
        if ( /\"/ ) {
            # this paragraph contains at least one double-quote
            ...
        }
    }
}
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