Will Medicaid cover hospital bills if i applied after birth?

So I’m 36 weeks. I just filed for Medicaid a few days ago (I know I should’ve done this a long time ago) BUT they said they’re sending me a paper to fill out & that way I can get the last 3 months of any medical bills covered (so all the way back to October) but I recently just had few complications & I’m worried I might go into labor earlier than I originally thought. Will Medicaid still cover me & my baby even though I just applied? Will this be counted as the “3 months back” ? I’m currently on my moms health insurance but I’m not sure that will cover it?