Messages back and forth between yourself and all other members are in "Chats."
While the website and app are completely synchronized, they have different messaging interfaces.
On the app, the default view for chats (tap chat icon) is the 'App Chats' tab and it will include all active conversations in the app.
If you are looking for a message sent or received on jwed.com, then you will find it under the 'Website Chats' tab.
Sent app requests and closed matches can be found by tapping the three-vertical dot menu on the top right.