Firstly, I wouldn't listen to her estimating that the baby is 4kg. I was told Nina was 'a decent size' bub, and she was only 2.98kg. The midwives were expecting at least 3.5kg!

Secondly, if you have a needle phobia, then accupuncture would not work for you. I don't have a needle phobia, but I was scared ****less! lol
There are plenty of nautral methods you can try other than accupuncture to get things moving along.
Congrats on reaching 40 weeks, and sending you lots of labour vibes.