Hi! You got some good comments. I was in your shoes a few years ago. I was told the baby was 10#2 at 37 weeks. She was born with no problem at 39.5 weeks and weighed 10#3, which would have put her about 9-ish lbs at the time of the u/s. Big babies run in the family and I later had an 11#5 baby, again with no problem. In the absence of gestational diabetes, babies over 10 lbs. are rare.
The hospital (midwives, docs) went nuts trying to push me into a c-section based on the u/s estimate. I declined because they gave me no evidence-- only anecdotes of their personal experience that they had seen shoulder dystocia and "it's really bad."
It can be really bad. However, the problem with their claim was that 1) there is no truly accurate predictor of fetal weight and 2) shoulder dystocia occurs unpredictably and 50% of the time it occurs in babies that are not considered macrosomic (big). So if they couldn't tell with scientific accuracy the actual weight of the baby, then as far as anyone knew, I wasn't actually at an increased risk of shoulder dystocia.
Most cases of SD are resolved with no injury. It would take 3,700 of scheduled cesareans on suspected macrosomic babies to prevent ONE case of permanent brachial plexus injury.
Sorry... long answer. Anyway, sorry you're having to focus on morbid stuff at this point in your pregnancy. Another thing to keep in mind is that there is a recent study suggests that inducing a macrosomic baby with Pitocin makes shoulder dystocia 23 times more likely.
I had to fight to give birth normally, unfortunately. I'm not sure if they're giving you the c/s push or not, but ask what you can sign in advance to let them know you understand their concerns if you are fine with labor taking its course. Good luck! –Jill