"Bring on" is used for medical conditions - headaches, asthma and so on. This is why the first sentence doesn't work. "Bring about" is used for more general situations.

"The sleepless night brought a bad performance on Tony." This sentence is not correct. It should be "The sleepless night brought about a bad performance from Tony. "Working out in the rain may bring on a fever." This sentence is correct! Bring on and Bring About are VERY similar but it is not about negativity. It really just depends on which event is being caused.