Thank you so much Hana for asking a great question. You have highlighted a lot of problems with our current healthcare system.
When my wife was young like you, that was exactly what she did. She was very sad, and she went to the polyclinic. And guess what the doc there told her? " just snap out of it, you are normal."
It can be extremely frustrating, when someone is trying to seek help and the other party wouldn't even listen.
Not all GPs and doctors are trained in mental health to the same degree, in terms of diagnosis and treatment. And the world of "mental health disease" can be so stigmatizing and confusing for the patients.
For a start, there are GPs, polyclinics, psychiatrists, psychologists, counsellors, family service centres. How does one even make sense of it?
Perhaps some helpful tips before we become lost:
1) Google is your friend. It does put a lot of information on your fingertips, it tells you your possible diagnosis and so on. But I would really take it with a pinch of salt, and see a doctor before you start imagining that you have all the symptoms listed on the DSM-criteria. I find that patients sometimes get stunned when we tell them a different diagnosis, or tell them that they do not have any diagnosis.
2) Go to IMH/NUH, they are big hospitals with well staffed and well trained people. Geylang and Queenstown polyclinic, like what Dr Julian Ng suggested, is a good start as well. They have branches there.
3) Find a GP with a special interest in mental health.
4) Find a private psychiatrist.
Take care and hope you find a doctor who will listen to you soon!