Basically if you had filed an extension and received the ITIN before the due date of the extension (October 15, 2016), you could have taken the child tax credit for your child. But, since you didn't extend, you had to receive the ITIN by April 15, 2016, which did not happen, so you lost the credit, and there is no going back and amending if you filed the return on time and didn't choose to extend originally. Unfortunately, this is one of those cases where it would have paid to talk with a professional up-front.
The final comment by SweetieJean has the correct guidance on this. The earlier comments Sweetie Jean and others were incomplete. The code section on this is codes section 24(e)(1).
