Regarding your unemployment compensation, the first $10,200 is not taxed at the federal level due to the American Rescue Plan enacted on March 11, 2021.
North Carolina has been updated for unemployment compensation and does not have any exemption for unemployment compensation.
Typically, what would happen is that a part-year resident state return would be filed for each state. You would complete both state interviews, entering the state where you lived as of December 31 last.
Any taxes paid in the other state would be a credit on the new resident state return. However, since Texas does not have an income tax, there is no offset.
Also, keep in mind that unemployment income is considered unearned income.
Amounts exceeding $10,200 in unemployment will count toward the $2,200 unearned income threshold. (Therefore, with no other unearned income, unemployment amounts greater than $12,400 of unearned income, $10,200 + 2,200 = $12,400 will result in a higher tax rate) See: What is the 2020 Kiddie Tax?
