Medical requirements appear in the 1927 regs (see pages 29 and on): Air Commerce Regulations Effective December 31, 1926
But those regs appear to have been developed from the Air Commerce Act of 1926. As far as I can tell, prior to that act civil aeronautics was self-regulated.
Edit to add that it seems that so long as a plane and pilot did not engage in interstate transport they were not subject to the Federal regulations. If they stayed within their state they were subject only to any state laws, if such existed.
