Automate creation of branch + pull-request
You want a RCS/VCS that handles the version incrementally for you. I'm not sure how this relates to CI as the idea is to Continuously Integrate instead of spawning more branches. I'm not sure what you're using for your PR's, so I'll use Atlassian Bitbucket as an example. In the response to pushing up a new branch you get back the url for creating a PR which has an API which you can call to create your PR.
Git commands will do the branching for you: 

# Get the latest description, usually based on tags : https://git-scm.com/book/en/v2/Git-Basics-Tagging
$branchName = git describe
# Checkout the new branch 
git checkout -b $branchName
# Push up the branch to origin
git push --set-upstream origin feature/$branchName


It's best to have a firm grasp of git when dealing with VCS. 
* https://try.github.io/ 
* https://git-scm.com/book/en/v2/Getting-Started-Git-Basics