I have made a checkout from Trunk, made changes and committed the changes back to the trunk. Now, I want apply those changes to a branch as well. Can I switch my working copy to that branch and then commit those files that have changed to the branch? I do have the list of the files that I have changed, and thus I know which files to commit. But I want to see if switching my local copy to that branch is the way to go.
You need to merge your trunk changes into the branch.
This is a very common use case and I urge you to read the whole chapter in the SVN manual regarding branching and merging so you understand what you need to do here and why.