while ( my $header = <$fh> ) {
  my $sequence = <$fh>;
  chomp ( $header, $sequence );
  $data{$header} = $sequence;
# or
  push @{ $data{header} }, $sequence;

# to read

print "$_ -> $data{$_}.\n" for sort keys %data;

# or for the hash of arrays

for my $key ( sort keys %data ) {
   print "$key : $_.\n" for @ { $data{$key} };
}