Amending after filing

I received a letter from the IRS that I still owed more money based on the child tax credit checks.  I do still owe that money, but as I looked at my filing status, I realized I had forgotten to claim my childcare costs for the year.  I would like to amend my return to include those deductions, and send the remainder in.  What is the easiest way?  I have a Notice CP11 to include with my payment, but can I also include an adjusted SChedule 8812 to show the deductions I did not claim?