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.
You've created a new human being, which by virtue of being a human being, has certain rights. We're already straying rather far afield from the basic information that the OP wanted, but since that's been covered, I'm OK with that. I'm in favor of the concept of Negative rights, in which the Right to life, for instance, is defined as: the right NOT to be killed. The right to property is the right NOT to be stolen from.
If You and I make an agreement to transfer ownership of a vehicle, the vehicle becomes my property, and is no longer yours. You haven't lost any rights, nor have I gained them. If you, or a third party then tries to drive off with my car, then you or they are violating my right NOT to be stolen from, and most certainly I can enforce that.