Division of property within 1 year of divorce?

Is it true that in NC, there’s a law that says that within 1 year of divorce, our house has to be divided such that both of us are no longer tied to the property together? I.e., I either have to refinance in my name only, or we have to sell?

No, this is not true about the law in North Carolina. You must be separated and living continuously separate and apart for one year before an absolute divorce can be granted. Also, you must have filed an action with the court for equitable distribution (property division) prior to the absolute divorce being granted or you are barred from ever filing for equitable distribution (unless you agree to property division in a separation agreement).