In your case, with a corrected 1099-G and a higher amount of unemployment received, you will need to amend your return.
When you amend and enter the new 1099-G, TurboTax will automatically adjust the amount so that you do not pay income taxes on the first $10,200 of the unemployment.
If your original return included that $10,200 then you will see the adjustment in your amount due or refund amount to reflect that change. Your AGI will not include that $10,200 for your state or federal taxes.
Follow the steps in this article: How to Amend
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