grep'll do what you want, in this case, but I would rather use a hash. (As your list of CDs grows, the grep operation will take longer, while a hash lookup will always take the same amount of time.)

my %dbfile = ();
open DBFILE , "$dbFileName" or die $!;
foreach (<DBFILE>) {
    $dbfile{$_} = 1;
}
close DBFILE;

if (defined $dbfile{$cdLabel})
    print "This CD ($cdLabel) is already in the database\n";
    exit; 
}
[download]

Better way to do it.