I am about 99% certain that panadol/paracetamol cannot be addictive, however it definately can have longterm effects on the liver and kidneys IF a person is consuming much more than the recommended amount...

I myself have given Aidyn panadol on quite a few occasions before bedtime, but this is of course only when he is teething and in pain, or if he is ill and feverish.

Teething can definately make a baby act strangely, and they can cry and scream for hours sometimes. It can be pretty hard for the poor little tykes, and pretty hard for others to watch/deal with as well!
So IMO I guess it could be quite likely that the strange behaviour of the bubby was indeed related to teething.