When I was a 16-year-old teen mom I was still in high school
DS had state insurance for a while, but then my parents insurance agreed to cover him, until I went off to college when we got state insurance for both of us (in Missouri).
While I was still in high school I had WIC, I used my pay stubs from my job at the YMCA. I dont remember how I got around them asking for my parents info, I do remember them asking.
State of IL has (or at least had) good daycare options for teen parents - Day Care Action Council I think it is called now - we paid like $5 a week or something for childcare. Parents paid for most diapers, got clothes hand me down or at garage sales/thrift shops with my money, mostly. I didnt have much money because I was still in high school and didnt have a lot of time to work.
My parents watched DS when I was working on non-daycare hours, and very rare times I'd go out with friends for a few hours. They did let me go to prom.
When I left for college, though, completely different story. We moved out of state. Because I was living alone and independent, I qualified for Pell Grants and took out some loans to be sure I could cover living expenses without having to work too much. I worked about 10 hours a week, besides taking 15 hrs/ semester and single parenting.
While I was in college my parents continued to pay for my car insurance, that was all, besides the occasional card with a $20 or some gas money pressed in my hand when I saw them. I still qualified for WIC but paid for all other food, diapers, clothes, rent, util, etc.
I know this child will be a blessing to your home, and you are gracious to be willing and able to help her out in whatever ways you can, while still pushing her to become the adult she must now be.