Yes, you have to split up your income for state taxes based on where you were when you earned it.
And yes, changing your business to an S corp makes a huge difference. Unlike a single-member LLC, an S corp is a separate legal entity. The S corp has to file its own tax return, Form 1120-S, separate from your personal Form 1040 tax return. Part of the S corp's tax return will be a Schedule K-1 containing information that you have to enter in your personal tax return. And the S corp has to pay you a reasonable salary, as an employee, for the work that you do for it. If you have not been doing that, you need to go to a local tax professional ASAP to straighten it out before the end of the year (which means in the next four weeks).
Various states may have special rules for an out-of-state S corp that is operating in the state. The tax professional that you consult should be able to help you with that, too.
