Narrow pelvis scared for delivery.

[Pud26]

I am currently 40+10 but at my 40 week appt I had a sweep and my midwife told me I had a narrow pelvis (due to my bone being in the way?) and didn't think the baby would fit through I was only 1/2cm dilated.
She phoned the labour suite who said just wait and see what happens in labour as my pelvis may widen.
I had another sweep at 40+7 and she said it was still narrow and I was now 2cms dilated.
I am due to be induced in 2 days time as still no sign of baby but I'm worried that they are going to make me go through the induction process and end up with a C section anyway... I am happy to begin induction but don't want to be in hospital for days with no progress... I'd rather have the csection and get on with it.
I am also wondering if the cause of no baby or pains is because baby can't get into the pelvis to begin his decent... (first time mum no idea if that's how it works)

Has anyone had or heard of this before and what happened with your labour?

[HavelockVetinari]

True cephalo-pelvic disproportion is very rare. The latest evidence (2017) shows that diagnosis is very problematic, and suggests that the management of birth should be the same regardless assuming the baby is head down. Please don't worry, your midwife is likely being overly cautious, but even if she's correct you may still have no trouble giving birth as your pelvic bones will soften and spread during delivery.