I would contact Brandon Grunbaum (wrote the book on on early baseballs history).
http://www.historyofthebaseball.com/index.html
..but I am thinking that this is not a baseball that was used in any pro major or minor league. Looks to be manufactured, but low end quality manufacturer. Would say 1920s. The stamping "professional" is just to give the impression of quality. A pro ball would more often be stamped "League" and have other markings. But, like you said, it is cool looking.