I have not yet started my period even though I should have by now. I have had some cramping and the other day I had some weird black discharge but have not had it since. I am on birth control but I missed 3 days of taking it. I am also sexually active.

This could be because of the missed pills. There's also a very good chance that you're pregnant.

Wait until your period is at least 2 weeks late, then test using first morning urine.