$dbh->errstr should give you what you want.

As moritz suggested, using exceptions can simplify your logic:

$dbh->{RaiseError} = 1; # only need to do this once
...
eval {
  my $sth = $dbh->prepare(...);
  $sth->execute(...);
};
if ($@) {
  # unable to insert, error message is in $@
  ...
}
[download]

Also, please use placeholders!