The child tax credit has nothing to do with your withholding. It's only calculated on your tax return.
The child tax credit can only be fully refunded ($2000) if you owe at least $2000 of income tax. If you owe less than that, but you have income from working, you can get a partial credit called "Additional Child Tax Credit." With $37,000 of income and filing as head of household, your income tax would have been about $1700, so you should have gotten most or all of the credit.
The child must be your dependent who lives in your home more than half the year, or your child that does not live with you but you are allowed to claim because of a custody agreement. The child must be under 17 on December 31 of the tax year. The child must have an SSN that is valid for work (generally this means they must be a citizen or have a green card.)
Look at your completed tax return. On the front page of form 1040, you should see the name and SSN of your child, and a check box in column 4 for "Qualifies for child tax credit". Then you should have a form 8812 attached to your return that calculates the credit. The actual child tax credit is on page 2, line 19 and the Additional Child Tax Credit is on line 28.
If your child is not listed on form 1040 or the child tax credit box is not checked, then you made a mistake when answering questions about your dependent. If the child is listed and the box is checked, but there is no form 8812, then you may have made some other error that the program thought would disqualify you.
