To be honest you sound like classic case, and sometimes it takes so long to show up in your blood test results that you've delivered by then anyway.
I was induced at 35 weeks last time around, and have been itching on and off since 7 weeks this time, although I've only had one bad blood test result so far thankfully.
I know entirely what you mean about the itching, and when I had alice i'd get up in the nigh and put my hands and feet in iced water to numb them, even though it was the middle of february!
Sadly in the UK they have decided to take this condition less seriously, and so induction isn't always as widely offered as it should be.
By 37 weeks, and with the symptoms you have I'd say there is everything to gain and nothing to lose by asking to deliver now.
Your tiredness is also a symptom, and may be accompanied (Sorry TMI) by darker urine, and lighter poo - I got very tanned looking (start of Jaundice!) though Jaundice is less common, and watch out for uper right quadrant pain - all associated.
I hope you find the website useful - when I first found it I cried with relief that someone was paying attention to a very rare but serious condition at least.
In the 3 1/2 years since I had alice I had some other complications (it can make you prone to Gall stones) and everywhere I have been treated I've ended up interviewed by junior doctors and medical students as nobody has heard of the condition!
Thats basicall why I'd err on the side of printing off the info you may need off itchymoms, and tellng your Dr what YOU want to happen when you see her.
If nothing else, if they do induce you tomorrow it'll mean the itching ends sooner - and that has to be a good thing!
Anyway I'm glad you spotted my post - I'll be looking out for you, and keeping eveything crossed that they listen to you and respond tomorrow.
Good luck and pain free, itch free, quick delivery wishes floating your way!
Cxx