There is always a way

You can go out and offer services such as cleaning someone's car for a few bucks, doing that with a few each day. Doing garden-work. That kind of thing. Try to do things that require you to be outside to be safe. And keep someone's phonenumber closeby if you need to call for emergency-help.
You can also check and see if there is a newspaper business around if you can deliver newspapers.
Are you studying anything in particular right now? Maybe you can get an apprentiship. It might not pay or pay much, but it will give experience and opportunities.
Waitering (maybe not a good idea if your mum goes to restaurants to eat, unless you're sure which ones she goes to and avoid those), cleaning hotels/motels/other places.
How have your brothers and other family members got over her throwing them out of the house? I assume they managed to move on in some way?
I would suggest talking to them about it. How you'd like to move on to get a job. I'm sure some would understand.
Try to get out and get into contact with real-life people.
She throws you out? Fine, then you can't take care of her anymore anyways

There are always ways for you to change your situation. You're never stuck.