No, you will not need to amend the 2020 tax return. The increased Child Tax Credit is effective on the 2021 tax return to be filed next year.
Any adjustments for tax year 2020 will be made by the IRS.
See this TurboTax support FAQ for information on the American Rescue Plan - https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-me/00/1393859
