Unfortunately
Childcare yea. The housing voucher maybe not. At least, even if you applied, it might take longer than 4 months to get it. I would suggest going in person and explaining to them you only have 4 months. Even if you do go to a shelter, not all are the same. Some are like an extended stay hotel,
You might find more help in this FB group regarding housing vouchers. For childcare, if you have an active PA case, you may qualify for a childcare voucher through HRA. If you don’t have a PA case, apply through My City. For housing, apply on Housing Connect, I don’t think section 8 is open, but apply for NYCHA. All long waiting times and lotteries, but doesn’t hurt to check it out. https://www.facebook.com/share/g/19tp8QjQ5C/?mibextid=wwXIfr
I don’t know much about the shelters, however in this FB group, I have seen families post about their experience. You can also reach out to your local Homebase, let them know your situation. However they help more if you’re being evicted and are in court. They might tell you wherever you’re staying legally can’t kick you out. But definitely post in that FB group, and read through some things.
I put myself into the shelter system when my baby was 2 weeks old. Unfortunately I do believe it’s the easiest way to get a voucher but they do have programs where you can live with someone and wait on a voucher but it could take longer than the shelter sometimes. You should definitely go to path they give you options other than the shelter
The easiest way to get a voucher i believe is to go to a shelter