Persistent Right Umbilical Vein

Went in for an ultrasound yesterday, everything looks good! Baby girl is growing perfectly and is measuring right on time. I have to go back for another ultrasound in 4 weeks. Everything looks good but they found out one of her veins didn't connect into the umbilical cord so they wanna monitor her over time to make sure she continue to grow okay and nothing goes wrong. The Dr said its nothing to worry about because it isn't a major vein it just shrivels up and dies once she born but I can't help but to worry. I was reading online about this and of course I read some things that made my mind go CRAZY ! Anybody experience this ? Hows your baby now? How was birth. I'm so scared.