can't update iPhone 6S to public beta 9.1
Follow this tutorial: http://www.imore.com/how-download-ios-93-public-beta

Your question being old, I'm guessing you might be interested in iOS 10 now, which you can obtain through a) a paid Developer account, b) invite to Apple's Public Betas, which should be coming soon, or c) an Apple Seed invitation, which you can't ask for.