No, you do not have to pay to amend your tax return. The change you need to make does not require the use of any special extra form or schedule that would require an upgrade to a paid version.
Wait until your original return has been fully processed before you amend, and make sure you have saved a pdf of the original return before you amend. (If you do not save it as a pdf, the amended return will overwrite the original, and the original will be lost forever)
See this TurboTax support FAQ for amending a tax return -
CURRENT YEAR
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-federal-tax-return-current-year/L7eS6o1qh_US_en_US?uid=lfunevhk