The Clinch is full of buffalo, the ratio of buffalo to carp is probably 10:1, but there are a few carp around as there is everywhere. It's just he buffalo are more numerous by far.
This time of year the river carpsuckers (specific species) run up stream and spawn in the shoals above the bridge.
However you could also find buffalo spawning now, a little early but they could start anytime.
You could have also hooked a large trout as well.