If your data file is really large then you should work on the data as you slurp it. I used an array because that is what your sample code used :)

while(<FILE>){
  next if /^matches messy header/;
  chomp;
  if (/matches some string/){
    my $next_line = <FILE>;
    # do something to $next_line here
    print "$_, $next_line\n";
  }
}
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--
Do not seek to follow in the footsteps of the wise. Seek what they sought. -Basho