Try to not lie and accept help. If you accept help you may not get kicked from the homeless shelter. I don't know the policy or how long it'll take to get out of your system. How comfortable are you in moving to a place that you know no one and trying to set up housing there? There are lists of HUD housing that have open enrollment. There are also places with fairly cheap studios but they're aways away. I just think it's so hard for you without a stable place and PHP. I hope you start feeling better soon.