It looks like I’m receiving EIC as well as some Child Tax Credits although I indicated while filing that my daughter’s mother would be the one to claim her and not me. Is that normal?

Not unless you are the custodial parent. If the child lived with you more than half the year, and you are either not married to the mother of the child and lived separately from the other parent, and you paid more than half the costs of keeping up the home for your daughter, you may be eligible to file as Head of Household, and you'd also be able to claim the EIC and the Child and Dependent Care Credit (assuming you were the one who paid for the child care). 

The other parent would be able to claim the Dependency Exemption and the Child Tax Credit.

If you aren't able to claim any of these credits or file as Head of Household, you should remove your daughter from your tax return completely to avoid complications.

See Guide to Filing as Head of Household to see if you qualify, and TurboTax will ask you all the relevant questions to determine if you can use this filing status.

[Edit 02/12/18 4:25 PM]

No. If you and the other parent live together, only one of you can claim the child for any tax benefit. The interview is confusing (it's designed for divorced parents). The second parent  (you) should not enter the child, at all.

 If you and the other parent live together, either one of you (but not both) may claim the child. You may decide between you which one will claim the child. Only if you can’t agree, do the IRS tie breaker rules apply, to see who has first choice. It may be worthwhile to prepare trial returns, both ways,  to see which way the family comes out best. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.