Are you actually working remotely IN Illinois, or are you working in Indiana for a company that is located in Illinois? If you are doing the work in Indiana, you are not working in Illinois. What matters is where you do the work, not where your employer is located.
If you are working in Indiana, your employer should stop withholding Illinois tax, and withhold Indiana tax if possible. For the year that you moved you will have to file part-year resident tax returns in both states, but in subsequent years you will file only in Indiana. If your employer will not withhold Indiana tax you will have to make estimated tax payments to Indiana.
If you actually do work in Illinois, or if you work mostly in Indiana but occasionally go to the company location in Illinois, it gets a little more complicated. If this is your situation, provide more details.
