Praise be to Allah.
This phrase (“I’ll show you”) is a threat but what may be meant by it is to make an official complaint, which is in fact what happened. We do not think that it matters if you tell them or not when the matter is investigated.
If she added any other words to it, such as insults or condemnation of the one who insulted her, then you should mention that, because she may have taken her rights by saying these words or more, and it is not right to punish him when the other person has already settled the score. Responding to an insult in kind is a kind of taking one's rights or settling the score, as al-Nawawi said in his commentary on the words of the Prophet (peace and blessings of Allaah be upon him): “When two people trade insults, the sin will be on the one who started it, unless the one who has been wronged went too far in returning the insults.” Muslim 4688. Al-Nawawi said: They said: If the one who has been insulted return the insult then the matter is settled, and the first one owes nothing to the second one, but the sin of initiating the insults remains on him. And it was said: He will be free from any sin if the other person returns the insult but the blame will still be on the initiator, but not the sin.
If what was said in response is not as bad as what was said, then the matter is not settled, however by responding, part of the matter is settled. This may remove or reduce the punishment for the one who insulted the other first.
Islam commands us to be just with all people. Allaah says (interpretation of the meaning):
“and let not the enmity and hatred of others make you avoid justice. Be just: that is nearer to piety; and fear Allaah. Verily, Allaah is Well‑Acquainted with what you do”
And Allaah knows best.