(sorry at work so cannot type Chinese)
yes, but you can only go public for Emergency services. "直接去掛號看診" is a big NO in NZ, not like China or Taiwan. If you gonna go public hospital just for a check up, and it is not life threatening, they won't be able to see you at least 4-5 hours later or not even able to see you. So what you need to do is: go see any GP, see how it goes, if required, ask GP to write a referral letter, and then you can get seen at public hospital.