Sorry, I still can't understand what you're trying to say. Say my wife and I have a daughter. She now has certain rights. Didn't my wife and I, by creating our daughter, also create those rights?

Rights arise as a consequence of particular states of affairs. By creating those states of affairs, we create the rights that arise from them as a consequence.

And agreements do create rights. If you buy a car from me, you now have the right to that car, a right you didn't previously have. The agreement created the right. I suppose you can argue that you always had the right to all possessions you justly acquired and that the right to the car is merely a consequence of a pre-existing right, but that weaker version of the difference between rights and agreements is too weak to make your point. (For example, you can certainly enforce that agreement against a third party who destroys the car that is only yours because of the agreement.)

Every valid agreement creates a new right on the part of all the parties of that agreement -- the right to enforce the agreement.