Shoulder dystocia

Anybody have any experience with this!? My first baby was born on her due date 8 lbs 10 oz and 22 inches long. When she was born her shoulder apparently got stuck in the birth canal for a moment and her right clavicle was broken. We were so scared she'd have complications because she didn't move that arm or hand for a couple of weeks, after a couple months of physical therapy she healed up perfectly! My midwife now is telling me I'll need to see a doctor for the remainder of my pregnancy to discuss c-section options because my first baby was on the "larger" side. I've never heard of this and am just curious is anybody else has gone through it? The idea of a c-section terrifies me!