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I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
If there is no court order giving your ex the right to keep your son, yes, you could, assuming you can do so peacefully. If you can't pick him up without disturbing the peace, then police would probably not allow you to take him. In a situation where neither parent has a court order, if police become involved, they will typically require you to get a court order before allowing you to take the child.
You could file for an Emergency Temporary Order in the New York Court, go before the judge immediately, and get a temporary order requiring the father to hand your son over immediately. That way, when you show up in North Carolina to take your son, if there are any problems, police should let you take him.
The problem is, if you just knock on the door without a court order, and the father refuses to hand your son over, there's not really anything you can do.