Is there a word to describe "a piece of information that you only want to know until you know it, then you regret you ever asked about it"?
The accepted answer given by Jasper Loy from the question "A common phrase that describes something that looks good but is actually not good" seems like it could apply here as well:
A poisoned chalice is something which seems good when received but actually does great harm.
Another related phrase is toxic knowledge. Though it is usually only used in discussing one's "genetic fate," I imagine you could get some traction out of it. At least one author has used it to mean, "knowledge that people seek which is ultimately bad for them."
I'm not sure if this will fit the purpose you have in mind, but I'd suggest "a can of worms."
To open a can of worms means to start a topic that might be more than you can handle. This makes it very similar to the myth of Pandora's box.
An online example for this particular idiom is: "When you brought that up, you opened a whole new can of worms."
I read that, born in the 1920s, this expression alludes to the image of opening a container and finding an inextricable (and thus complicated) tangle of worms used as bait.