Yes, you're (over)due to take a week's break from the pills and let yourself have a period, to clean out your uterus. Go ahead and take that break. You haven't hurt yourself, but stop the pills now for a week. Also, take Advil, it might be a crampy period.
It's unusual that you had a period even though you kept taking the pills. Because that happened, you should do a couple of things: talk to your doctor about getting a stronger pill, and take a pregnancy test. Bleeding while on the pill is an indicator that the pill doesn't give you enough of a hormone load to be effective as birth control.
The pill works by giving you enough hormones that your body is fooled into thinking you're pregnant and stops ovulating. If your body was doing its natural thing enough to have a period, you might also have ovulated during the three months. If you've been having sex in that time, since the pill seems to have been too light a dose for you, get a home pregnancy test to check if you're pregnant.