Hey Paahi,
You can also check what other options are available for homeless people or people with health/mental health problems where you live.. There are some organisations that may help... (both with shelters and finding accomodation)
There are also people who could maybe help you, you do need to get out and meet them kinda!!
Some people also live in tents or such temporarily, or 'squats' (where unused property is 'taken over' by people who want to live there - sometimes these can be 'punks' or drug scene, sometimes more like artsy people/creative scene..) Sometimes the church or other organisations can help..
It's good if you can talk with parents and find some agreement, yeah.. so at least you know where you're at.. You can be an asset at home by offering to help with laundry, dishes, cooking, in the garden etc. And by learning to economize/budget and not be wasteful with money, food, energy etc and time..
And if you're making an effort to look for a job or to get better (go out, find help, eg psychologist/support group) this can help too.. If they don't understand sa, you can show them books/articles or the documentary about sa etc.
Sometimes you can also get a place to live in exchange for helping at a farm or babysitting or teaching languages or such.. Some jobs come with a place to live too (eg touristy jobs in hotels or such)
Or you could find a significant other with own place etc. (long-term option, you do need to get to know them better first)
There are a lot of options, it partly depends which country you live in!!