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I was told something similar, but they were WAY off. My baby, supposedly very small, weighed 7.5 lbs and was perfectly healthy. These machines can't tell us everything. Often the panic they cause is far more dangerous than not using them.
Your body knows SO much more about growing a baby than any doctor or machine does. Please do not let them rob your baby of the opportunity to grow in the safest place it will every be-- your womb.
Whether you believe in evolution or design we can all agree that whatever created us is smarter than anything we could possibly think up or begin to understand, so why trust a man over your body? It makes no sense to me.
I do know how scarey it is to trust in nature when it is your baby concerned. Believe me, I know. I've miscarried 6 times and have done everything possible to have two healthy babies. ALong with that has come an incredible amount of research (I have enough college biology/ chem to enter a master's program in nursing, though I am not a nurse now -- I'm not just making this all up).
You are right to worry that if they go in after your baby she might not be ready and you might be kept from breast feeding her. That isn't good for her, surely. Also, hospitals are THE place to catch antibiotic resistant bacteria. Your womb is safer. Why does your doctor want to induce? Most first time c-sections are a direct result of induction in cases where a mom would have eventually birthed naturally.
Pick up a copy of The Thinking Woman's Guide to a Better Birth by Henci Goer. It is the definitive research work (and very readable) about all hospital practices and their statistical outcomes in regards to birth. It's an eye opener.
Doctors are concerned with lawsuits and their careers (understandably -- I don't blame them) more than what is actually best for your baby. In a court of law, more intervention, while proven to be more dangerous to mom and baby, looks to a jury like a doctor did everything imagineable to help the situation. In reality, births go much better if they are left to Mother Nature and disasters can follow unnecessary interventions.
Sorry if this sounds like a rant, but from all the research I've done in trying to protect my own babies I just really feel a mother's protective fierceness about birth interventions.
I wish you peace in this journey and a healthy, relatively comfortable end of pregnancy.