I can connect to my server if I type in Rust Console: client.connect localhost:28015
I cannot connect by using IP: client.connect xxx.xxx.xxx.xxx:28015, (thus it does not show up in the server list.)
and i can see the server works from the rust+ app

You have to port forward the ports with your router/modem. Depending on what ports you have set in your "server.cfg" file. Also make note of what the local IP is on that computer you are trying to host the server on and make sure that you are forwarding the ports required for that computer otherwise the server will not show up in the list for public players.

-Castwolve.