Ouch. I went over the handlebars pretty hard twice on pedal bikes when I was a young lad. Once going down the steep wall of a gravel pit, once at speed when my chain broke and my foot went straight down and hit the road. Both times I landed on my chin/chest and slid. Ouch. It is remarkable that nothing got hurt other than skin. And yes, that feeling when that bike beneath you is suddenly behind you--yikes! Of course, those experiences didn't stop me from skateboarding down a steep hill with no helmet or any padding anywhere. DOH. Again, nothing injured other than skin.

Anyway, glad you are not too seriously hurt. Get some new rubber--old tires will kill you, one way or the other.