No, there's no permanent physical damage that I'm aware of.

The caterpillar sting was intensely painful for an hour or two, and then afterwards for a couple of days I'd have random relapses of less severe stinging at the site.

The wheel bug bite was so long ago that my memory of it is a bit faded. I was bitten on the foot when I put my shoe on. The pain from that was like getting snapped in the foot by a searing hot bear trap, kind of all at once, and then it simmered down. However, I couldn't comfortably wear a shoe for a day or two afterwards and I had to limp around because it was painful to walk.