Wiring through an ethernet wall plate
If the ethernet wall sockets exist, and have wires connected to them, where do those wires go? Since the common layout of an ethernet wiring system is to have all wires going to a central point with a switch, or patch-panel and switch, the simple solution to connecting bedroom and living room is to connect the existing wires at the central location (plug a patch cable in between "bedroom" and "living room") or (depending on what you actually need) just put a switch there if one is not already there and plug all the cables into it (so everything is connected.) Normally the only place you need an isolated wire is from the WAN (connection to the outside world) to the WAN port on your router - everything on the LAN (your local network in the house) can be connected to a switch so that it is all interconnected.

Otherwise what you need to do depends greatly on whether or not you have conduit connected to the boxes that the ethernet is in, and the physical relationship of the rooms and ethernet wall plates in the rooms, and the type of construction of the walls.