In order to establish Head of Household status as a married person, you need a qualifier for that status who also qualifies as your dependent.
It is possible to claim a child for the purposes of this credit without claiming the child as a dependent, but careful documentation is required in order to establish relationship and residence of the children. Be prepared to offer school and medical records to verify the residence of the child. Documented statements by churches or landlords may be acceptable.
If you are 18 or younger, and live with your mother, then you may be a qualifying child for your mother, for instance. You cannot claim the EITC for your child, but your mother may be able to claim EITC for both of you.