Dreamhost, they have their own custom control panel so it makes it hard to do things.
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Dreamhost has mysql databases...
Permissions can be limited. For example, my host does not allow adding new databases outside of their own control panel.
However, no host limits mysql usage to the point where you cannot modify tables-- it would be pointless.
There may be no default editor setup, but you could try to install one (like phpmyadmin), or just use text commands.
In your PHP, you can use commands like mysql_query("CREATE TABLE ...") and go from there.
PHP Code:mysql_connect("host", "user", "pass") or die(mysql_error());
mysql_select_db("database") or die(mysql_error());
mysql_query("CREATE TABLE IF NOT EXISTS `code` (
`codes` text NOT NULL,
`used` tinyint(1) NOT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1") or die(mysql_error());
Did it happen to work out for you?