I started my period and May 22 and ended it on May 28 my boyfriend and I had unprotected sex on May 28 and 29th we are trying to conceive a child and on June 1 and second I am having brown discharge and also read discharge and cramping feeling nauseous diarrhea and mood swings could I be pregnant

Maybe, and hopefully so. The fly in the ointment is that those symptoms aren't unique to pregnancy nor an indication of pregnancy. The only really sign of pregnancy is a missed period. Which is going to be more then a month away. If you don't get your period within two weeks of when you should then take a home pregnancy test using your early morning urine.

The waiting game sucks I know, but that is the best and only course of action, besides still trying.