the relay isn't in that pic. it's the square black thing that probably came in the same bag as the fog switch. It connects to "H"
I have a relay on mine that came with my civic fogs.
Anyways, I managed to hook mine up similar to yours however I didn't need to connect those two wires together. I'm still a bit puzzled but glad it works now.
I went crazy with the wiring when I did it last year, and connected it to an oem switch with an oem wire connector.