Work in one state/live in another? How does it affect remote work?

I currently live and go to community college ( completely web-based but is an in state college) in Louisiana.

I’m currently looking at fully remote jobs in my current field ( patient coordination/billing and coding) as I will be in Washington DC for the next year taking care of a family member.

How would that work tax wise? Since the remote jobs I’m looking at have no state specific requirements meaning I can be anywhere in the US, will I be paying DC taxes?