First i would recommend you start getting some pre-natal care. You can go to a polyclinic and get a referral to Kandang Kerbau Hospital. You will be seen @ Kandang Kerbau Hospital at subsidized rates.
If you want Mt A, i believe the gynaes there are private and could be of higher rates.
As for confidentiality, I am sure hospitals have their regulations regarding patient's privacy and won't be giving out un-necessary information to asking parties.