You need to add both states. When you do the state returns you will tell each state what portion of your income was earned in that state. You will not be taxed twice on the same income.
However, you will have to pay for two state returns if you use TurboTax.
Since you mentioned W2 and not 1040, I read it as asking whether you should be withholding NC and/or GA taxes this year. Since you are a now a resident of GA, you should be withholding against GA state income tax. This generally applies even if you are working connected remotely to an NC office.
From the sound of it, you still have NC listed as your state of residence, so do get it fixed ASAP. You will be stuck filing a nonresident NC return to get what's been withheld returned to you, but will very likely be hit with a GA penalty because you haven't withheld GA income taxes this year. It could be beneficial, though possibly not kosher, to pay NC income tax based on your W2 and then use that payment as a credit against GA taxes. After all, you have been paying state income tax all along, just unknowingly to the wrong state.