Pregnancy Testing

I had a baby almost 3 years ago. I did the test to see if the baby would have DS or any other birth defects. They told me that some of my levels were high and sent me to a specialist. When my specialist was looking he offered a more thorough blood test that would test if I carried the gene for DS plus 1000 other deceases (I can’t remember the name of the test). I also can’t remember if that goes for all my pregnancies or if I have to take it each pregnancy. when he called me he said that I do not carry the gene and my pregnancy should be healthy. Has anyone done this testing? Was it for all babies or just per pregnancy? Me and my husband were looking to try again soon. Of course we would love regardless just curious.