Any moms have babies who’s head measured big?

I am so conflicted! 😥 my regular OB sent me to a maternal fetal medicine doctor to get an opinion on his plan for my birth and the MFM doctor did not seem on board with his plan at all. My baby is measuring big (3-4 weeks ahead) and has been since I was 30 weeks. She is also weighing a lot and I have a lot of extra fluid (polyhydraminos). Anyways, my OB told me that he thinks I should be induced at 37 weeks or have a csection at 38 weeks. When I was at the fetal medicine doctor he said there is no reason for csection or induction until 39 weeks at the earliest. I am 37 weeks and my babies head is measuring 41 weeks and she is 8 pounds 8 oz. I feel very nervous about letting her get bigger over the next few weeks because I don’t know how a birth like that would go. I really want to avoid an emergency situation like her shoulders getting stuck or an emergency csection if possible. Anyone have anything similar?🙃