You'll need to start a paternity action anyway, so you might as well do it. You'll need a court order to amend the birth certificate, and while you're in there ask for a custody order, the court to issue a visitation order and child support.
And yes, since everyone you slept with during a period of time needs to be DNA tested (they should be demanding a DNA test), it will probably be a long drawn out process. And if you test someone and they turn out to be excluded, they should be coming after you for the cost of the DNA test.

