How did I not answer your question? You are saying you don't want to use a third party site like Twitch/Ustream etc. So that means you have to use your own server. There's no other alternative. Either use your own server, hosted locally or on another computer in your own LAN or on a VPS, or use a third-party streaming site like Twitch/Ustream.
If you have Red5, then set OBS to stream to Red5, and then set JWplayer to receive from Red5. I don't know how to use Red5 or JWPlayer, so I can't give you specifics. You'll have to google around for it.