An amnio is voluntary. It is also generally done much later in the pregnancy and only if there is enough reason to believe there might be a problem with the baby. All you have to do is ask yourself two questions. "will it matter what the amnio says? would I terminate this pregnancy based on the results?" If the answer is no then the only reason to go through an amnio is if the baby is going to be born premature and they need to check the development of the lungs. Remember, it is your body and you don't have to do anything you don't want to. You have to give permission for any tests to be done on you.
At 11w 3d I went for the NT scan and bloodwork. They came out normal. I go back next week for the second round of blood tests and another U/S. Is this the screening you are referring to?