I think the problem is that they don't tell you what exactly they do with your blood.
I mean, it's a part of your body. It will regenerate but still, they have it and do something with it (tests).
So your paranoia might be a signal that you want to know exactly what they are doing with that red body fluid you send them. But that isn't possible. It's sent to a laboratory where they analyse thousand of samples every day in large machines and with the help of computers. It's all very efficient and nobody working there cares if the blood you sent is yours! Really, they don't! I know doctors personnally and they work so much, they don't have time to think about you, they only search for the disease in your blood.
They would say: "It's in your interest to send your own blood. If you send someone else's blood, the results won't tell us about you and if you get sick but you sent your father's blood we won't see your disease and you might be in danger."
So they trust you. but your mother - as a doctor - knows that. That little trick was her idea you said? It's a typical bad idea doctors have. Because she doesn't care whether it's your blood or not, but you care. And I think you are right to care. She's overstepping her authority here.
You have to take this in your own hands if you want the paranoia to stop. You need to take back control. If you can, find a way to make sure it's your blood and your blood only that is sent for testing.
One more argument - this time a logical one, not an emotional, power-structure related one - to help battling your paranoia:
The laboratory couldn't know if the blood is from your or your father even if they did a DNA test.
Your DNA and the DNA of your father are different but only slightly. to find out that it's not your blood but his is very expensive and they only do that after
you have already become the suspect of a crime, in order to prove it. yet, it's a medicinal laboratory, not CSI: Las Vegas.
I'm not trying to call you stupid, not at all! You say your English is bad, but it's very good. So you're smart but if you're smart you need to take responsibility (because you can
) maybe the paranoia is just yourself trying to push you towards taking that responsibility.
Tell your mother that it is not ok what is going on right now. Then you have to do what you have to do to make sure it's really your blood that is tested. Maybe then the paranoia will stop!