Researchers can find information on more than 27,000 medical people with some Indiana connection at the Indiana University School of Medicine Ruth Lilly Library Historical Databases.
There are actually two databases but they can be searched together. The search interface reaches every word, not just names, but otherwise doesn't seem too flexible -- and good luck if you're looking for a surname that is also a common word! (My workaround: since all the results come out in a long single list, you can do the search and then do a control-F search on the name with an initial capital and check "match case.") An extra benefit here is that a search of the database will pick up names of individuals who were not themselves doctors or midwives, but who are mentioned in their biographies, obituaries, or letters.
My search for "Everts" (a big surname in 19th-century La Porte County) produced 17 interesting results and lots of leads to follow about the whole family. Here is where the individual researcher's skill will be tried. Sourcing is not clear, even when large blocks of text are quoted. And the supposed drop-down list of "sources" is just a list of individual words as they appear in the text. Occasionally what appear to be source citations, or scraps thereof, do appear in association with text.
The compiler writes quite properly, "We offer these databases as guides to further research in the history of Indiana physicians and Civil War surgeons." But it is not always easy to tell where a given fact or quotation came from. As a result, beginning genealogists may give up and cite this database as their source, rather than keep on looking for the original record, book, or article. Any citation of course is better than none, but this would be poor research procedure except as a stopgap aide-memoire. Visit this site often, but be prepared to do more work afterwards.
Harold Henderson, "Good news for those with medical ancestors in Indiana," Midwestern Microhistory: A Genealogy Blog, posted 29 May 2013 (http://midwesternmicrohistory.blogspot.com : accessed [access date]). [Please feel free to link to the specific post if you prefer.]