Geetrick is a ship between My Chemical Romance's Gerard Way and Fall Out Boy's Patrick Stump.

Along with Petekey it is believed that the Geetrick relationship took place during Warped Tour '05

To summarize:
Geetrick is a "fictional" relationship between Gerard Arthur Way and Patrick Martin Stump.

There was barely any photos for Geetrick so I got some fan art too:

(If you can't see what's in this, it's Patrick and Gerard hugging)

Oh by the way, the quotes on fictional for all of these chapters are saying that they've never been proven or denied so they are quote unquote fictional.