C.M.
I don't know about medica because I've never dealt with it.. but I know that medical assistance in my area will cover prior bills. So if you have to go to a doctor to confirm pregnancy they will likely cover that once you're on the insurance. Otherwise you can talk to the business office and they will work with you with payments according to your income. I know that when I found out I was pregnant with my son and was at my first appointment they still offered to check my eligibility for assistance despite the fact that I had insurance.
Most places are always willing to work with you! Just ask what you should expect when it comes to the medical bills until you recieve medica and I'm sure they'll be able to fill in the gaps for you. Your social worker might be able to help you on that one too.
Good luck! It does sound like you'd probably be between 6-8 weeks, but there's no telling really since the early start was kind of strange.