Am I being unreasonable

I’m pregnant and went to the ER for for a threatened miscarriage. I found out the the father cheated . He had already decided that he wanted to stay with the girl. When he got caught. He turned into someone I didn’t even recognize in that moment . All of the sudden he claimed he is not the baby daddy. Well he is my one or was my one and only boyfriend. Then he was like well the timeline doesn’t add up . Then all of a sudden he wants custody. So I blocked him. And decided if this baby is healthy or ends up healthy. It’s getting my last name . He isn’t coming in the delivery room. Too much stress.