I almost caused a car crash while driving home today

Here's a top-down image of the whole scenario.

This happened at the same four-way junction I go through every day. I stopped at the stop sign (my car is the white rectangle). I looked left then right and I didn't see anyone coming so I went forward. Then I looked right ahead of me and I saw someone on my right (the yellow rectangle) so I quickly pressed on the brakes. I ended up stopping right in the middle of the junction. The guy who I almost crashed into just gave a "WTF" look and then he drove to the right. I have no fucking clue how I didn't see him earlier. I'm pretty sure that this is the closest I have been to being involved in a car accident so far.