My doctor is now pushing for a C-section as she says that the umbilical cord(naal) is wrapped around the baby's neck. I want a normal delivery. Should I do as she says?

Of course, trust your doctor on that! Umbilical cord wrapped around the neck is definitely not the best situation to be in. Get over the pressure to have a normal delivery. The first and foremost priority at this point is the safety of your child.