Is it common to get a false negative test?

I suspect I'm pregnant but not sure, my period is late for a couple days (it never gets late) and I have other symptoms too however last week I was throwing up a lot and took a test that said I wasn't pregnant. It wasn't my morning pee or anything, it was in the middle of the day. The day my fiancé ejaculated inside of me was about 3 and a half weeks ago. Maybe when it's too early the test doesn't work? I'm really dumb when it comes to this subject, need help.