family service centers are free for singaporeans I believe and they are almost everywhere in singapore. Usually in the neighborhoods etc! There are people who are practicing to become counsellor as well who are willing to do pro bono work. Another free option, although it is only catered for short term. And I also suggest trying other sorts of therapy rather than just talk therapy.
Things like movement, art, music, play therapy etc can all be beneficial and helpful. Over The Rainbow has free events by donation where one can explore some of these therapies in SG as well.