My residence is in North Carolina but I stay in Georgia during the week for work. Which state gets state withheld taxes?

My wife and I moved to North Carolina from Georgia at the end of March 2019. My job is in Georgia and I stay with my brother in Georgia during the week. My W-2 shows my address as my brother's address and taxes were withheld for Georgia. Is this correct? I believe NC would consider us to be residents of NC since we are registered to vote in NC and our cars are registered in NC. Have our taxes been withheld for the wrong state? If so, what can we do about it?