Overstaying 90 day visa, pregnant in Spain

Hello - looking for some advice. My boyfriend and I are living in Spain - we have been here about a month and I am on a 90 day shengen visa from the US. I am pregnant around 5 months and am planning on staying here to have the baby (for many reasons i won't go into here at the moment). Is it possible for me to use public healthcare now and/or after I overstay the visa? I have read briefly that pregnant women here illegally are not turned away from care, but i have no idea how i would go about getting this situated. Any recommendations or advice would be greatly appreciated, thanks!