You are responsible for your child's health and well-being.
Part of that responsibility means securing financial security too. And if the father does not know, how can he meet his responsibilities (there are laws).
Can you be sure that he would not accept the news and not want the chance to be responsible too?
No matter what you imagine might be the outcome here, can you live with the consequences of NOT telling him and your child (when old enough).
You got over the pains in the delivery room, so now go for your next challenge and do what is right. It probably won't hurt as much as you imagine right now.
Good luck, and keep us posted.