You are misunderstanding the use of grep.

In your example, grep will always return $l unless $m happens to be 0 or an empty string.

Instead of grep, you probably want a regular expression.

  if($l =~ /\Q$m\E/)
  {
     print "We matched\n";
     print OF "$$l";
  }
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You probably also want to use chomp in the outer loop to remove the line ending from $m.

You are also writing the file multiple times with different lines commented each time. You might want to generate a list of the expressions to match at the beginning and then loop over the file once.