Your situation sounds incredibly difficult; I can’t even imagine being homeless with a child in a Massachusetts winter. I’m so sorry.

I really second what other people have said about checking a lawyer/the consulate/etc. to see if there’s a way to stay with your family in England.

Have you looked into Headstart preschools at all?

https://www.mass.gov/guides/head-start-early-head-start

It looks like maybe their national toll-free number is 866-763-6481

They are meant for low-income families and are free, and sometimes have other built in services/support. From what I’ve seen they tend to be really high quality childcare, too!. If you can go anywhere in the state, you could maybe call around to see where they have space (I’m not sure how enrollment works). It would give your child a safe, warm, developmentally appropriate place to be during the day, and might allow you to start work again. They might also have resources to help you find shelter/get other benefits, since helping families experiencing homelessness is one of their priorities.