If your egg is fertilized very shortly before your period (bleeding) week should normally start, can you still have your period? Is your period not a definite sign that you aren't pregnant?

Correct. If you are pregnant then you do not get a period. A period is the shedding of the uterine lining when one does not get pregnant. Sometimes women have vaginal bleeding during pregnancy but this is not a period. This is not normal though and should be evaluate. If you think you might be pregnant check then check a home pregnancy test. They are cheap, reliable and available at any pharmacy.