Do I get paid for same day cancels if I go home sick or otherwise same day cancel that very same day myself (as a teacher)

No. If you cancel same day (Sick or other reason) and a student cancels same day.  You cannot expect to get paid for that.  Many times the student finds out from friends etc. that you weren't there and demands a makeup lesson.  It is very difficult for us to argue the point that the teacher called in a same day cancel and the student also called in a same day cancel on the same date and you the student have to pay anyway and don't get a makeup lesson.  Just doesn't make any sense to them. "The teacher called in same day too.  How is that fair?"