Honestly, the poly or GP should be your first stop since they deal with pregnancy cases all the time and will know exactly which medicines are safe for you. If you're worried about the distance to KKH, most polyclinics have OB records on file anyway, so they can check what's suitable without needing to refer you elsewhere. The wait at a poly is usually shorter too, which matters when you're unwell and pregnant. If they feel you need something they can't provide, then they'll refer you to KKH, but I'd say start local first.
I always go to GP whenever I am sick and they have pregnancy safe medications! Just remember to inform the doctor that you’re pregnant.