It's hard for me to say simply because you had unprotected sex so here's what I think you should do: first, get a pregnancy test. Since you don't know when your period is supposed to get here, get a test that tests earlier. I like First Response Early Response Six Days Sooner.
If that comes back positive, then I think you can certainly blame your symptoms on pregnancy.
If the test comes back negative, with all of the symptoms you're having, I believe you should accept it as negative and see a doctor if the vomiting is still happening because there's a possibility that you have an infection or a bug. And, if the vomiting is related to anxiety, then you should definitely talk to your doctor about that.