I don't think you're following what bradgrafelman is saying:
your problem is not that "the results won't echo in the html".
the problem (or so it seems) is that, at the very beginning, you are doing something that completely prevents your results from being what you want.
$_SESSION['auth'] = 'yes';
// do you really want to do this?
// if you're using $_SESSION['auth'] to authenticate the user, then this makes no sense:
// you're automatically declaring him an authorized user, without even checking anything.
// but I digress...
$_SESSION['username'] = $userName;
// $userName does not exist at this point.
// even IF $_SESSION['username'] _did_ have the user's name, it now has _nothing_
// (because you just assigned it the value of an undefined (and therefore empty) variable.)
// MAYBE (???) //
// does $_SESSION['username'] already have the user's name?
// (say $_SESSION['username'] holds the value "Bill")
// Maybe you're trying to do this?
$userName = $_SESSION['username'];
// would print "Bill".