Custody and child support?

We get money from the gov but it's in his name and hes not giving me any. we just broke up yesterday. he doesn't have a job and i do but not enough to support me and my 10 month old. i want to have shared custody b/c i love him, my baby loves him and he is a good dad to him. but i want child support or some kind of help. can i get that with shared custody and with him having no income? i don't have money for a lawyer so my ? is how do i get started? do i just walk into the courthouse and tell them i need help with custody and child support or is there a number i call? any advise or personal stories much appreciated.