Ran over a large truck tire fragment, what damage to look for?

I hit a large chunk of truck tire on the highway today, nothing I could do, the guy in front of me swerved last minute to avoid it but I had someone in either lane beside me so I had no choice but to hit it dead on. It damaged my spoiler and bottom of the grille which really stinks, I can't even pop it back into place. Going to take it to a body shop but the biggest concern I have now is potential damage under the car since I ran over it ... my guess would be it broke up or flipped when my spoiler hit it and was kind of flat for the rest of the runover because there are barely any scuffs anywhere under the car. What else should I look for? Is there any serious protection of the oil pan or anything or is it just that kind of cardboardy cover that I assume is for aerodynamics? I'm going to have an actual shop look at it Monday but I was hoping to jack it up and look myself yesterday just because it's really bothering me, plus I want to know if I can drive it to the body shop. I drove it about 8 miles home after the incident, drove fine, no lights, no leaks, or anything. Only thing out of sorts I can see underneath is the fastener in the photo ... it looks like it holds the cover panels together but it's loose and just wobbling there.