Coolant does feel a little oily, it does not mean it is mixed with oil...
The best thing to do now is to clean the engine really good, and try to pinpoint the exact location of the leak (s). other than that, you might start an expensive repair that you might not need.....
From the picture, it does not look like the timing cover. it is not the water pump because it is on the other side of the engine.....
it is either something simple like a coolant hose/ pipe squirting coolant everywhere, or more serious such as an engine freeze plug, or leaky headgasket..., but again, i am just guessing here. the starting point is to clean the engine, raise the car until you find the source (you might use a mirror for the hard to see areas), and go from there...
or you could drop it off at your indy
Good luck !!
Edit: WOW, i just noticed you have 2000ish posts, so you probably know what I've said already.,,,,ignore my post