Probably nothing to worry about. If you looked up your local IP address, you probably gave him a none routable address such as 192.168.xxx.xxx. This number and the others like it won't go out on the internet, but would stay on whatever local network he's on. For example, on your network at home your router or modem is on 192.168.1.1. (You and I also both have the same "home" IP address of 127.0.0.1.) There is nothing for him to look up with the number you game him, nor can he use is in any meaningful way.
If however you gave him your public IP address for some reason, then you could have problems depending on who he is. You might also have a problem falling for other social engineering schemes depending on why you gave it to...