I've been telecommuting in VA for a good portion of the year. I've paid taxes in VA for the past several years. Back in August I moved to NC, and I'm now updating my W4 form and also getting my State ID.
I've lived in NC during August, September, and October, but my withholding was done in VA. I'm looking for advice on updating my W4. Should I withhold more money for state taxes for the past 3 months, and will I get the VA tax withholding back at the next return?

Would taking an additional amount out of my paycheck to make up for those months work the same as making an estimated payment?

How does that work? Thank you for the help!