Ovulate and period question?

Can you ovulate the day before your period, have the egg fertilized and still have your period? I don't know when i ovulate, I have been having blood tests for the last year on cycle day 21 and 28 and they have NEVER detected ovulation, but i know that i have ovulated after day 28 because i had a miscarriage 6 weeks ago. I have PCOS and my cycles are all over the place they can be anywhere from 10 to 60 days. Could someone please tell me if it's possible to ovulate the day before your period or during your period and get pregnant when on your period? My DH and i have been trying for baby #2 for almost 18 months.