No, you should be able to allocate your income properly to VA and NC without needing a corrected W-2.
Since you moved during the year, you will be filing part-year resident returns for both states. When part-year resident returns are involved, your income will be allocated to each state based on when you lived in that state and what you earned during the time you lived there.
You will not be filing a tax credit on either state return for 'taxes paid to another state'. That only applies in cases where you lived in one state and worked in another and both states were taxing the same income.
Just be careful to review the income being reported to each state as you go through them. The NC return will determine your total NC income tax by taking a ratio of income earned only while a resident of NC divided by all income earned for the year.
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