I claim my son i made 48000 so the eitc i didn't qualify for the credit But after the tax break my earned income falls under 40000 do i have to ammend for the Eitc

What "tax break" are you referring to? The unemployment exclusion? The unemployment exclusion does not reduce your earned income, because unemployment benefits are not earned income. But it does reduce your Adjusted Gross Income (AGI), and that could possibly make you eligible for the EITC if you were not eligible before.

If you are talking about a tax break other than the unemployment exclusion, ignore the rest of this post and reply back with more details about what specific tax break reduced your earned income.

Did you already file your tax return with unemployment income but without the unemployment exclusion? If you already filed your tax return without the unemployment exclusion, and without the EITC, then yes, you will have to file an amended return to get the EITC. But you must first wait until the IRS recalculates your tax return for the unemployment exclusion and sends you the resulting refund. By then more information will be available about how to file the amended return. For more details see the following announcement, which the IRS just issued today.

IRS to recalculate taxes on unemployment benefits; refunds to start in May