Assuming you're in an ethernet switched network rather than something funky like a token ring: Even the great Wireshark is limited in what it is able to see because it runs in the same confines as what you're trying to build - its host PC.
Unfortunately, your PC can only see the packets that hit its network interface. This means that in a layer 3 routed network you're unlikely to see any packets that aren't intended for you, unless of course your PC is the router.
You'll need to look into SOCKS5 proxies and the like to achieve the level of network transparency your question infers. While implying a small bit of network and configuration overhead, a proxy will provide you the most visibility into the traffic you're after.