'Knackered' is British and Irish English for 'exhausted'. 'I'm knackered' just means 'I'm shattered, I'm worn out'. It comes from the older noun 'knacker' (someone who slaughtered worn-out horses), so the metaphor is 'worn out like an old horse'. If your teen uses it, they are using everyday British English. The word is mild and acceptable in most British conversations, though older speakers may find it slightly coarse.