Oh no... the way the pill works is, it puts synthetic hormones into your body for 3 weeks... and then as the hormones are metabolised out of your system, you get what is called a "withdrawl bleed" - the drop in progesterone (progestin in the pill) causes your uterus to shed its lining.
Some women will get a period 2 days after stopping the active pills. Some will get it 4 days later.
Not having it after 3 days is not too strange - I wouldn 't be surprised if by now you've gotten it.
But sometimes you CAN skip a period on the pill. I don't know why. The first month I went on Desogen I didn't get a period, but I wasn't pregnant. But then years later I skipped a period on Yasmin and didn't think anything of it because of the Desogen thing, started a new pack, took a pregnancy test a few days later, and it was +++. So it pays to test to be sure - but it CAN happen and mean nothing. You just start a new pack at the normal time.
As for 21 day cycle... no... you count cycles from menses to menses, not first day of active pill to menses. (Although I know people often start the pill the first day of their cycle, which can make the first cycle a little short I guess...)
So say you take the active pills... 21 days... get your AF 3 days after stopping (that's when I get it)... you would start a new pack of pills 4 days after that... and get another period 24 days after THAT... the time between periods is 28 days. But when you are first starting out, your first cycle may be few days short if you do a first day of period start, or off a little either long or short if you so a sunday start, depending on when your period starts relative to that sunday.
Hope that helps. You're probably fine, don't worry!
I'm a bit confused 
