It looks like github has a simple UI for creating branches. I opened the branch drop-down and it prompts me to “Find or create a branch …”. Type the name of your new branch, then click the “create” button that appears.
To retrieve your new branch from github, use the standard git fetch command.
I’m not sure this will help your underlying problem, though, since the underlying data being pushed to the server (the commit objects) is the same no matter what branch it’s being pushed to.