If your family won't help you, the only way to do it is to do it yourself.
If you think you can try facing your fears, then do it straight on like i told you - slowly. You just have to remember to not put it off. If you say you'll do it next week, then do it next week. If you keep putting it off you'll see no results.
That is why therapy works better because they make sure you do it. If you feel you need that extra push then the first step is to - no matter how much this might make you cringe - take that part time job. Screw your mother, this is more important than her if that is how she's going to treat you. If she punishes you, ignore it. She doesn't deserve you being a good little girl to her. Learn how to take the bus if you don't already know how, as this will help you in getting to therapy while the job helps pay for it. Who knows, your mother might even grow to respect you more because of it. If that isn't enough, there are probably other financial aids to look at when you go to therapy.
The next step would be the phone book - call someone that sounds right for you and book an appointment to see them. I don't care if you have to sneak out of the house to do it. It may take a few therapists to find one that's right for you, but keep sticking to it. You'll find someone just right eventually.
Good luck.