My guess is that you experienced margarita burn, so not from the lime juice alone but its reaction with UV. As long as you’re not in the sun, probably fine to handle.
This is literally what the article at the top of this thread is about, why are you presenting this information as if it's unrelated? Additionally, OP said it was chemical + sunburn, not lime juice alone.
https://en.m.wikipedia.org/wiki/Phytophotodermatitis