i had accupuncture and a 4.5kg+ bub lol
i dont have a needle phobia though, but i was still pretty nervous about it.
As people have said already the needles are very fine. Most of them i didnt feel go in. Some i did but it was no worse, and probably less uncomfortable than a blood test. Definitely 1000 times smaller needle or at least it seems like it.

If your eyes were closed you probably wont even know most of them are in.

I wouldn't necessarily go by guessing re your bubs size either, it can be way out.

Maybe you could have a look at the articleon the main site about natural induction methods and try some of those?
Evening Primrose oil, sage oil belly rubs, reflexology, there are lots of natural induciton methods you can try apart from accupuncture.