Hi mama, congratulations on your pregnancy! The long waits at KKH are pretty standard unfortunately, a few mums I know went through the polyclinic route and said the first appointment itself can take 3 to 4 weeks to come through, and then on the day there's still quite a bit of waiting even with an appointment slot. It's the trade-off for the subsidized care, but I understand it's frustrating when you're anxious and just want answers!
On the transvaginal ultrasound, some discomfort is normal in early pregnancy scans, but what you're describing (pressure that's really uncomfortable even after you've fed back) does sound like it went a bit far. A good sonographer should be responsive when you say something hurts; they can usually adjust their technique or take a break. The fact that the doctor seemed distracted about other details too makes me a bit concerned about the overall attention you received.
Honestly, I'd say it's worth flagging this with your next appointment or even calling KKH to request a different doctor if you didn't feel heard, you have every right to do that. Your comfort and peace of mind matter, especially in your first pregnancy. If you're considering private care instead, do weigh up the costs, but don't feel stuck with an experience that didn't sit right with you. Worth a chat with your GP or the polyclinic doctor too about your options and concerns.