I live in Tseung Kwan O, too. You can go to the Tseung Kwan O Po Ning Road Health Centre (1/F for pregency) which is located opposite to the Tseung Kwan O Hospital. All the check-up are free of charge. They only accept new case on Wednesday morning (9:00am). Just go and have your first check-up. Later, you will be arranged to deliver your baby at United Hospital at Kwun Tong.
For me, I have prenatal check-up there for 3 times already. I was aked to do the ultra-sound at Tseung Kwan O hospital next time (22 Apr). Your baby is a few days older than mine. You better have your first check-up as soon as possible. Maybe, you need to do the ultra-sound at your second check-up. All mama should do the ultra-sound between week 20-24 (for the public clinic) the latest. If there is something wrong for the baby, the doctor will recommend to do the 提早引產 before week 24.
For me, I will move back to Hong Kong (western district) and stay with my Mother from July onwards because my mother wants me to deliver my baby at Queen Mary Hospital. I talked to the nurses about my case at the Health Centre (I just told them I will move) and they said it's OK for that. They can transfer my record to 贊育 to follow up when the time comes.
If you want to do the check-up at private clinic, you can do so. Try to find some highly recongized doctor. You will have more confidence. Make appointment as soon as possible, some famous doctors need 3 weeks advanced booking. Hope my information can help you.