Experience with Induction

So im wondering if anyone has experience with induction due to babies size. I had an ultrasound yesterday at 37 weeks and baby is estimated at 9lbs and his trunk is measuring 41 weeks. She is concerned about me going past 38 weeks and him getting any bigger and us having to deal with shoulder distocia and other issues. I know ultrasounds can be off so I told her I wanted to give him time to come on his own and I scheduled the induction for 38 weeks exactly. My first two came and 38w4d and 37w6d so im hoping this one will come on his own before the induction. Im also nervous because my first 2 were only 7lbs and he has been gaining a pound a week now. If his ultrasounds are accurate he could be like 12 pounds 😵. Im just looking for some stories of inductions for this reason or any reason really as I've never been induced! Thanks 😊