I feel your pain. My home life hasn't been much better. It's good to get out tho. Accept your friend's mom's offer because being in a safer and happier environment will help give you more confidence and happiness. And that may be all you need to get yourself a paid job. Make sure you tailor your resume to each job you apply for, so for example: if it's a bookstore including a section about how you love reading and your favourite books. Anything that may make you stand out from the crowd will definitely help.
But it's hard times finding a job (I know, I'm looking again myself), so if something paid doesn't come through, take a volunteer job whilst you're still looking. Any experience on your resume will definitely help you.
And don't give up your boyfriend. If he makes you happy and helps you through then you stick with him. But definitely try to get out sooner rather than later, it could be the biggest step you need to getting your life heading down the path you want it to.