@ElizaBennett - The situation you describe is called a chemical pregnancy. I went through one, and it wasn't pretty! I got positive early pregnancy test results, and then a few days later I got my period.
My doctor said it was a chemical pregnancy. Basically, that's a really early miscarriage when the positive pregnancy test (elevated HCG levels in your urine or blood) was the only evidence that you were pregnant. He said if they had done an ultrasound, they would not have seen anything, because it was so early on that a gestational sac would not yet have developed.
Once there's something they can see on the ultrasound, it's considered a clinical pregnancy, and he said that happens about a week after your missed period or when you are about five weeks pregnant.