Yes, you can get these taxes back. Since Indiana and Kentucky are reciprocal states, you are not required to file a Kentucky return unless KY withheld taxes. Your question suggests that they did not, but by filing a return, it appeared that you owed KY taxes, when that was not the case. To fix this, file a KY amended return with a zero income, but stating the amount you paid towards your tax "due" from the last two years. Then, you will put in the explanation that you are an Indiana resident and should not have paid KY state tax. To back this up, provide a copy of the Indiana returns for each year. Kentucky will return the taxes you paid in mistakenly.
Next year, when you use TurboTax, you will want to say no to the question if you worked in another state besides Indiana. This is because KY does not tax you, so this will prevent the program from generating a return you don't need.
Finally, there is a possibility that you could be entitled to extra refund on your Indiana return as well. While the reciprocal agreement covers state taxes, it does not cover local taxes, which you may have paid in KY where you worked. However, IN does provide a credit for local taxes you paid in another state. If you did not take advantage of this credit, and you paid local taxes in KY (box 19 on your W-2), then, you can open up the Indiana State Return, click on the Other Deductions and Credits tab, and look for the selection "Local Taxes Paid to another State". See the screenshot below:
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