If you have mass messaged your members in the past, with the old messaging system, your messages would have gone out to the members, but unless your members replied, your messages only showed up in each member's mailbox but not your own.
With this new messages plugin, all those mass messages you sent out in the past now show up in your inbox as a "conversation". So you now have hundreds, even thousands of "conversations" in your inbox, thus loading down your inbox.
If you just let it load (it will take a long time), they should eventually show up. And unfortunately, this new messaging plugin does not have a bulk delete feature, so you now have to delete those thousands of messages one by one. This will take weeks, if not months to do. Because after you have deleted one, it will take up to or over 1 minute for the next message to load, so that you can delete it.
I ask the developers to PLEASE update this plugin to be able to bulk delete messages!