She told me that something completely unbelievable had just happened.

Literal

[topic-は] completely cannot-believe thing [subject-が] just happened-[just-now-ところ-feminine-なの] [quotative-と] me [to-に] told-[explanatory-んだ].

Multilayered modern colloquial sentence. 信じられない ('unbelievable,' negative potential of 信じる) modifies こと ('thing') — 'an unbelievable thing.' ちょうど起こったところ uses ~ところ in its 'just X-ed' sense — 'just happened.' The feminine sentence-final なの marks the quoted speech as her words: の as nominalizer + な (feminine softening) gives a typically female-coded explanatory tone. The outer 言ったんだ uses the explanatory んだ, framing the sentence as the speaker's report of the event. The whole thing is a vivid casual narrative line — someone retelling a friend's surprised announcement.