Does informing the police that my mother is my maternal aunt, then swearing to that, count as a "Ghamus Oath," knowing that I was confused and no longer know how that happened?

What you did was inform of something contrary to reality, which is a lie. If you had an excuse, such as fear of harm, then there is no sin upon you. But if there was no excuse, then it is obligatory for you to repent, and it is more prudent to make expiation for this Ghamos oath. You can resort to allusions (Ma'areedh) to avoid lying.