Oh coco - big, big hugs. Thank goodness you got checked out.
Someone I worked with went through this I think (I can't remember the name of the condition, but it was liver related and caused itchiness, so assume it was the same thing), and she was induced a few weeks early. Her DD was born very healthy and is now a gorgeous toddler.
Didn't want to give you false reassurance so just did a quick google and reputable sources suggest that the risks associated with actively managed OC are little different to other pregnancies. Plus lots of stories of babies born at 37 weeks just fine, home in 24 hours. I know that won't take away the worry though.
Hope the hospital are looking after you well - and we're all here for as much virtual hand-holding as you want xx