The Gemara (Bava Kamma 2b, as explained by Rashi) seems to agree with you that we can't learn a Torah-level law (דברי תורה) from Prophets and Writings (דברי קבלה), but it clarifies that it is possible to use it to learn גילוי מילתא, to use the Prophets and Writings to clarify what the Torah means. We can't use Prophets and Writings to learn something new is permitted or forbidden, but we can use them (as in this case in the Gemara) to prove that "goring" refers to damage of the horns.
In other cases, we do learn actual laws from Prophets and Writings, such as the laws of Purim which were instituted in the book of Esther. But in these cases we aren't learning Torah law from Prophets and Writings; the laws from there are on the lower level of דברי קבלה. The ability to create laws isn't dependent on the fact that it's written in the Bible; even Chanukka has its laws, just like Purim, despite the fact that its laws aren't instituted by a prophet.