There is a place called Büro für medizinische flüchtlingshilfe that offers qualified medical help for free and you don't need to take an appointment.
It is twice a week opened, on Mondays and Thursdays from 16.30 until 18.30.
Hinterhof, Aufgang 3, 2. Stock
U-Bahnhof Mehringdamm U6/U7
Telefon: 030. 69 46 746
I wish you all the best for you and your coming baby!