ovulating & having period?!

So I started ovulating 3 days before my period (I'm a day 21 ovulation gal anyway) but now period starts and I'm still getting high fertility readings 3 days in! I've google searched this, it seems it's rare. Is it possible to get pregnant if this is happening? What does this mean? Although it would explain why after 2 yrs of trying we have not been able to conceive (as generally we avoid sex during period)...anyone out there have insight on this?