Ohhh - it sounds like a tough time. Dont stress too much about the drs - hopefully your GP will help you out.
I'm sure its not too late to change to public care if you want to. Generally speaking my experiences with the public system have been very good (alwyas a few exceptions) and there is no point in being mucked around pillar to post by people you are paying!
The Nuchal test does need to be done when you said - and I'm sure it must be horrible having people tell you that you dont know what you are talkingabout! I'm sure your GP could give you a referral for the test if need be - I got my U/S referral from mine, and she would have given me any other referrals I needed.

I hopet hings come right for you soon - you dont need all the extra stress in your life!!