So I\'m working in a branch, make some changes, and run git merge master. I get a merge conflict on one of the files I modified (which I know how to deal with),
When you attempt a merge, all files that can be automatically merged (e.g. where you don't have any changes in your local branch but which have been modified on the source branch), are automatically merged and staged. Files which could not be automatically merged are updated in your working area with conflict markers and you have to fix them.
Git always assembles new commits in the staging area before committing them. The merge does the same thing. A new commit with all the changes from the source branch is created in the staging area. In case of a conflict, this process of updating the staging area is interrupted and control is given to you. That's why this happens. Once you commit, a "merge commit" will get created in the repository that has both the source and target branches as parents.
As for " I don't want any of these not-by-me changes to get committed.", why did you do a merge at all if you don't want any changes?