If your income is too low to receive the full $2000 child tax credit, you can qualify for the "additional child tax credit" which is based on earned income, that is income earned from working. (Non-working income, like a pension, unemployment, or investments, do not count for this credit.)
Self-employment IS earned income for the additional child tax credit.
But more importantly, if you work a side job, you must file a tax return and report the income, even if you don't get tax paperwork, regardless of whether or not you qualify for a credit. You must report all your income, and then you get whatever credits you qualify for.
