The Child and Working Family Credits

Here is my situation, I rent with my girlfriend and our 2 year old son. My girl is claiming him for the dependent she is the head of household. My girl made over 100k but I only made 20k last year. My girl dont qualified for the earned income tax credit or EITC for the federal credit. But I on the other hand think I do qualify for it since my income was small. Is this true??? because I made less, had earned income, no investments, and I'm a US citizen. Can I still claim my child for the federal credit EITC? If my girlfriend is claiming him as dependent for the child tax credit. I did turbotax and on the federal part it says I dont qualify for the child tax credit due to someone claiming him that is good that is what I want. I also received the EITC. But why on the state part it says I qualify for the child tax credit and working family credit. But I do NOT want that since my girl is claiming the dependent. Please help?

Here are some of the screen shots. The 1st pic is correct I don't qualify for the Federal Child Tax Credit, but why does it say on the 2nd picture that I qualified for $2110? That does NOT make sense? I don't want to claim that because my partner will claim the child for the child tax credit.