When filing a Form 1040-X, you need to explain any changes you have made in Part III of the return. In this case, it looks like you added a Child as a Dependent and the Child was also used as a Qualifying Child for EIC purposes, so you should have an explanation of this in Part III.
In addition, you need to attach Schedule EIC to your Form 1040-X. I think this is the main thing they are looking for in your case.
