Does Tumor Marker Blood Tests Can Produce False Positives Or Even Negative Ones?

Hello, I am 46 years old, no history of ovarian cancer on either side of my family. I have had 4 children. My periods for the most part are every 30 days. But, first 2 days it is pretty heavy. My obgyn did an ultrasound at 3 weeks after period (so pretty late in cycle), & uterine lining was at 20 & one 3 cm cyst on each ovary, and ovaries a little swollen. Nurse called & said I needed to get a blood test to see whether the cysts were benign. She actually really scared me & told me that Ovarian cancer was the Silent disease & that s why we needed to have the blood test. What do you think about this? I have heard that the tumor marker blood tests can produce false positives or even negative ones? I m wondering if they were jumping the gun.