It depends on your status. If you are a Non Resident Alien, then you would need to use http://Sprintax.com to file a 1040NR. You are considered a nonresident if you do not meet Green Card Test or Substantial Presence Test.
If you are a resident alien, eligible to file the regular 1040, then yes, with income of $22k and having children, you would be Eligible for the Earned Income Credit, since your SSN is valid for employment with authorization, as long as you still have that authorization.
You would not be eligible for the Child Tax Credit as you would not have any type of tax liability after a standard deduction, however, you could be eligible for the Additional Child Tax Credit which is worth up to 15% of your taxable income minus $2,500.
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