Have your mom write a letter saying all she is goingto do is put a roof over your head and that's it. Stating the baby is your responsibility and as soon as you are able to get a job you will pay rent. Have her sign that paper. Then take it to the welfare department fill out the paper work you need to and explain to the worker how your mom won't help you at all except for providing a place to stay till you are 16 then you will need to find a job and day care. That's will probably be the way it'll work where you live. That's the way the county is here in california.
You will probably have to depend on your mom for food until your boyfriend starts working.
Just a recommendation but, can you do babysitting or something like that to make some money? Your boyfriend could mow lawns or do some landscaping. You do not have to be 16 to do any of these things and it will really help your mom and you both with food.
My bf will start working when he turns 16 and I can't work because I'm underage and staying home with the baby
Unfortunately her income is counted against you. Not reporting her income is fraud and could get you in trouble if you were caught.
Is your boyfriend working? Are you able to get a job? I'm asking because it's getting harder to get food stamps.