Hit a "aready hit" deer, what should I do?

I was driving my 2011 Nisan Altima at 11:00 at night. I was driving 100 km/hr and to my right two vehicles where pulled over with their hazard lights on. This common where I live so I kept driving. Out of no where I saw the carcass of the dead deer and tried to swerve to avoid it but I wasn't fast enough (and panicked) and the right side of my car ran over the center of the deer. I kept driving eager to get home to see the damage. Using a flashlight there doesn't seem to be any damage to the car, just fur stuck on by blood and blood splattered paint. The smell made me sick.

Even though I didn't kill the deer I feel like me keeping on driving wasn't what I should have done. I didn't do anything wrong right, since the deer was already dead? Also, even though I can't see any damage to the car on the outside, what should I look for (or feel) while I drive it?