I assume you mean not just the same program, but the same instance of it running on the same machine.
Do you care about the case where you're connecting back to yourself via the network (perhaps you have two network cards, or a port-forwarding router, or some unusual routing out on the internet somewhere)?
If not, you could check whether the arbitrary address resolves to loopback (127.0.0.1), or any of the other IP addresses you know are you. I'm not a networking expert, so I may have missed some possibilities.
If you do care about that "indirect loopback" case, do some handshaking including a randomly-generated number which the two endpoints share via memory. I don't know whether there are security concerns in your situation: if so bear in mind that this is almost certainly subject to MITM unless you also secure the connection.