Are my priorities visible to anyone else?

Yes, priorities are shared based on your sharing settings.

Your manager, if you have one, will always see your priorities. By default, your priorities are also shared with your team, that is, other people who share the same manager as you. However, it is possible to make individual priorities private just by clicking the padlock symbol.

You can change your global privacy settings by visiting the Settings page and editing the section, "Who is allowed to access your priorities?".