No, it is very unlikely that you can be pregnant. You had sex too close to your period to be fertile even if the pills failed, the 1 hour difference in the pill taking time is ok, it is much too soon for implantation bleeding.
If you are new to the pill, you are correct. It is not your period you are experiencing. The pill stops the uterus wall from preparing for pregnancy. When you start the white pills, the uterus will just bleed because the hormones that stops it from bleeding is withdrawn, not shed its lining and excrete it like with a period.
This is why the pill is often used to treat menstrual, hormonal and PMS problems.
Best of luck!