There is no plugin for menu. Menu management is natively built-in to WordPress.
It sounds like the issue you are having has more to do with your user role than anything else. It may even be the reason you do not seem to have control over the menu.
First, check that you are indeed logged in with the Administrator account. That means logging out and then logging back in. Before you log out, though, in the dashboard, go to Users. Look at the users list, see how many users there are, and see which user name has the Administrator user role.
If you are truly locked out of being the administrator, take a look at this thread, which has some advice about how to change the user role of an user within the database using phpmyadmin.
Once you have confirmed that you can log in as, and indeed are using, an account with administrator user role. Test your menus, themes and plugin control again. If you are still having trouble, post here again and I'll continue to help you troubleshoot this.