When it's best to take a pregnancy test can actually depend on the brand you buy and how sensitive it is! For the most accurate result, you should wait one week after your first missed period, but there are some tests that you can receive an accurate positive on the first day of your missed period (putting conception at about two weeks prior). Since pregnancy tests work off the levels of hgc in your body, you can get accurate positives if you wait about two weeks after having sex, as it takes 7 - 12 days after conception for hgc levels to develop in measurable amounts. The most sensitive tests can report an accurate positive about 8 days after conception (which can occur up to a couple days after having sex).
The first response digital pregnancy test is advertised to be able to detect pregnancy as soon as six days before your first missed period - however, this is only a 60% accuracy. The accuracy of the test was statistically calculated to be 99% when it was two or less days before the first day of your missed period.
Since your period has some flexibility of being 3 - 4 days off your expected and it's only been one missed day so far, for the most accurate results, I would usually suggest waiting a few more days. However, since you had sex right after your last period and it's been about a month, it should be pretty accurate if you take it now.
The first test you took was likely accurate, but it could depend on what brand you used. There's more about how to know if you used a test that would have been accurate in the link below.
ScarleTeen has a wonderful breakdown of pregnancy tests that should answer all your questions better than I just did, so you can find it here: Peeing on a Stick: All About Pregnancy Tests
Since you're having a lot of anxiety around this, have you thought about adding another form of contraception to help you feel more at ease? Do you have any questions about your options or need some help figuring out how to go about getting an appointment to discuss a prescription with a doctor?