On my profile, when I try to edit the tag badge I am aiming for, there is only one tag option. Do you need to unlock other tags?
Yes, you can only track tag badges for tags for which you've posted at least one post (answer or question). If you haven't posted yet, you can't track a tag badge at all. Due to caching, it may take some time (at most 24 hours) for tag badges to become available.