The child and dependent care credit and the child tax credit are two different credits. As for the child tax credit, if you were eligible for it the software would have automatically included it when you prepared your tax return. You can see the amount of the child tax credit you got on your Form 1040A on line 35; on Form 1040 line 52
If you filed without entering the child and dependent care credit, you need the Tax ID or Social Security number of your childcare provider. If your original return has been fully processed and you have received your refund, you can amend to put in the childcare credit. You go to Federal>Deductions and Credits>You and Your Family>Child and Dependent Care Credit.
If you need to enter additional information, delete something, or change something on the the tax return you already filed, you have to wait until your return has been fully processed, then you can prepare an amended return, called a 1040X. You cannot e-file a 1040X. It must be printed, signed and mailed to the IRS.
After you print, sign and mail your amended return—1040X— to the IRS wait about 3 weeks and then you can begin checking on it at the IRS website. Be aware that it can take at least 3-4 months for an amended return to be fully processed (or sometimes even longer.)