Claiming my son after his father did by accident

My fiancé filed for his taxes. When it got to the questions about our son, he clicked that there was an agreement that the mother was claiming him on her taxes. Well, it told him since there was an agreement he was not eligible to claim him. It still asked for our sons information and he provided it (after I told him that didn’t sound right and he assured it was fine since he clicked the other parent was claiming him). When I went to file for my taxes, it rejected me. It said that his SSN had already been used and he was already claimed. My fiancé went over his taxes and it looks like he received EIC for our child. This has turned into a nightmare.. we didn’t get back any child tax return since he didn’t “claim” him. So I’m going to send my tax return in through the mail and claim my son. After my fiancé gets his full return back, he’s going to amend his. I guess my question is, will my tax return be denied by the IRS after they receive it? Do I have to wait for my fiancé’s amendment to go through to receive my refund? I know that amendments take 12-16 weeks. How long will it be before I see my tax return back?
My son has lived with us equally as we live together, but we agreed I would claim him as I was pregnant most of 2017 and have countless amount of OB and hospital bills to pay from my pregnancy. I also have sole and physical custody of my child as we’re not married and there is no court order, so in WI the mother has sole and physical custody until a court says otherwise.