W-2's are often incorrect, particularly for state withholdings, and your entries in TurboTax don't have to match the document.
Technically, all your income is VA-Sourced, so your corrected W-2 showing 100% to Virginia is not incorrect.
First prepare a Part-Year Resident Return to Virginia and report the income earned in Nov/Dec after moving there, and the total amount of tax paid there.
Then prepare a Part-Year Resident return to DC (Jan-Nov), reporting the wages earned while living there, and the amount of tax paid to Virginia on those wages. This will be most of your income, and you may need to do some math.
Here's more info on How to File a Part-Year Resident Return and Allocating Income for a Part-Year Resident.
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