oh I see it's on the sweet shoppe designs facebook page. Facebook pages are all public (this goes for any page there is no way to make them private) so if you comment on a post there people can see it. Groups can be set to private though so there is more privacy there.
I understand how you feel because I'm pretty private too and like to keep things separate.
Whenever you see the little globe icon beside a date that means the post is public (so that goes for posts you comment on for friends etc) and anyone could end up seeing it.