For any who may google into this page
>> You are not eligible for EIC if your unearned income is more than $3600
This isn't true. There is a maximum investment income limit ($11k for 2023), but there are many kinds of income that are neither earned income nor investment income, for example, IRA and 401k distributions, gambling winnings, most non-commercial rental income, etc. These kinds of unearned income count towards the AGI limit ($53,120 for married, family of 2 in 2023), but they don't count as investment income.
See the IRS EIC qualification simulation for your specific situation. It is at:
https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit-eitc
