No. You cannot use the Free Edition for self-employment income. You need online Premium or any version of the CD/download. With self-employment income you need to prepare a Schedule C. Free Edition cannot do that, nor can online Deluxe do it.
Or—-Use this IRS site for other ways to file for free. There are 8 free software versions available from the IRS Free File site
https://apps.irs.gov/app/freeFile/
https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922
https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax
https://ttlc.intuit.com/questions/1901340-where-do-i-enter-schedule-c
https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct
The self-employed tax credit was only available for tax years 2020 and 2021.
Go to this IRS website for information - https://www.irs.gov/newsroom/tax-credits-for-paid-leave-under-the-american-rescue-plan-act-of-2021-specific-provisions-related-to-self-employed-individuals