How do I get my first apartment

I have a son he's 3 months old I'm staying home to take care of him I don't have much help at all, his dad works full time but only makes $11/hr we are staying with my mom in a very small room and I don't feel welcome here I won't go in to detail but I just want us to get out of here I don't know what to do besides going to work full time and putting him in daycare which I dread to do so soon when I'm breast feeding. I don't know what to do. Public housing is not accepting applications I don't know what to do I have no credit no nothing. I only have savings I saved for my son. I don't know what to do I'm losing it I cry everyday I just want to be here for my son and give him a place to grow and not this small room but what do I do how do I get low income housing or anything I don't know what on earth to do or where to god damn Start please someone help me please