A hand written agreement means nothing unless the court signs off on it. She can say whatever she wants. She doesn't want to go to court becaue then she is FORCED to give you visitation. Without a court order she can play all the games she wants to and there is squat you can do.
If you don't do a paternity test, get court ordered child support and visitation/custody, don't expect help when you come back here in three months or three weeks griping that she backed out of her agreement which she signed.