Sorry, you cannot just take a board exam and start practicing medicine. Law, you can.
In 2014, 60 apprentices took the bar exam (out of 83,963 total examinees). 17 passed.
Almost all states do require law school nowadays, and you don't have a prayer of getting reciprocity to practice in another state without it.
https://priceonomics.com/how-to-be-a-lawyer-without-going-to...
https://www.americanbar.org/content/dam/aba/publications/mis...
http://www.slate.com/blogs/business_insider/2014/08/02/state...