Turn to these free online primary sources:
Medical Heritage Library
A consortium of medical libraries, including Yale, have put parts of their collections available online. Over 300,000 freely downloadable primary source books, many from 1780-1923. On the Medical Heritage Library website, you can find access to American and State medical society journals.
National Library of Medicine (NLM) Historical Collections
Great primary history of medicine material, including digitized books, images, archives, and moving images (aka movies). Freely available movies include the 1952 film All My Babies: A Midwife's Story and the 1966 Maternity care: labor and delivery.
Home to a huge variety of resources, including Moving Pictures, for free use. Not limited to history of medicine, but lots of possible primary sources here on childbirth in America. Make sure, if you pick a source from here, that it's uploaded by a library or other institution! Film possibilities include the 1970 Not Me Alone: Preparation for Childbirth, which includes Lamaze, or a 1930s film showing a Caesarian section, Childbirth with Caesarian Operation (Filmed in a Hospital).
A huge online repository of freely downloadable books and journals, from a collaboration of libraries including Yale. Not limited to history of medicine, but lots of possible primary sources here on childbirth in America.
Digital Public Library of America
This site pulls in sources and archives (like letters and diaries) from many libraries, museums, and other institutions, as well as big databases like Hathi Trust and Internet Archive.
This is a selected list of sites related to topics involving the history of reproductive health. This is by no means everything!