No because you were on your period

You can get pregnant any time during cycle.
It all depends on when you ovulate.
Have you missed your period?
All you can do it take a test &find out.

Even if did ovulate during my period and the egg was fertilized, there wouldn't be a uterine lining for it to stick to, right?

I don't think you can ovulate during your period.
But some women can ovulate very soon after your period.
Say you ovulate 4 days after your period ends-
you have a chance of being pregnant because sperm can live
inside of you for sometimes up to a week.

Just wait a while &then test.
That's the only thing you can do.

You are protected through your week of sugar pills. You are not pregnant.