sorry, but it may be improper for each of you to claim 1 child under the tax rules
since you are both the parents
apparently, you live together for the whole year then
the IRS says it's the parent with the highest AGI that's entitled to claim them.. so if you both filed as head of household claiming one child you both misfiled. one gets both the other files as single.
some states recognize a common law marriage - but most require that it be recorded.
you need the help of a tax pro because there are significant penalties for claiming tax credits you are not entitled to.
