If you are not comfortable with it, you can go to Lorong 8 Geylang. There is a Hotel 81 that charges $10 for one hour and you can just get one hour. That gives you a clean room to have a proper bath, poops and a short rest in a bed. You do not have to worry about prying eyes at public toilets. You don't have to do it everyday. Maybe once every 2 days. For $10, it's not so expensive.
I was once poor, down and out. But I survived. You will too. Good luck.