Nope, not fossilized coral: the top part has too much variety in the design, and it doesn't go all the way through. If it was coral the top would basically be like a cross cut of a bunch of tubes gathered together, which you would see throughout the rock. (VERY basic explanation, I'm an amateur!)
The GOOD news is, it's way cooler. What the heck is it?? I'm curious to find out too!