You will file as a part-year resident of NC and a part-year resident of NY. Your NY return will, however, include all of your 2016 income. 

Even if you were a resident of New York for 1 day, NY uses your entire AGI to calculate your tax on NY income That is why your W-2 shows all your income as "NY". 

It isn't, however, as bad as it appears. They calculate what your New York tax would have been if you earned everything in NY, but then prorate that tax based on how much of your income was earned while a NY resident. 

For example, if the NY tax on your entire 2016 income was $10,000 but only 30% was earned as a NY resident, your NY tax would be 30% of $10,000 = 3,000.

Why do they do this? So they can tax your NY income at the highest possible tax rate, based on your entire AGI.