Can you have your period and still be pregnate?

i went to the health dep for a prego test! my and my fiancee are trying to have a baby! the test came back a very faint (almost unnoticable) positive.so they made me anouther app for 2 wks.. im having all the signs of pregnacy..tired,nauteious,sore ,crazy dreams ect....but i was 5 days late on my period and yesterday i started having pink blood then it got heavier and red...my fam has a history of having periods while prego but only the 1st 2 months...can i still be pregnate?