Temporary Assistance in NY state

I'll be 30 weeks pregnant on Saturday. I have yet to find a job, although one might be lined up shortly. But it's part time and doesn't pay much. My parents aren't doing that great financially right now and suggested that I apply for temporary assistance to pay them rent since I'll be staying in their house, and for wic, etc. My baby's father is involved, we just aren't together and don't live together. But I was told if I'm going to apply for temporary assistance, they make me file for child support as well. But I'm not looking for child support from him because he will be doing his part already. If I tell him that he has to pay me child support it will just cause a lot of unnecessary conflict between us. Does anyone have experience with this at all?