In my experience, once you're late for your period, you can usually take a pregnancy test at any point in the day, and you'll get an accurate result. However, I do know a couple of people this wasn't true for! If your period continues to be late, then I would take another pregnancy test, but take it in the morning with your first urine of the day and trust that result.
I too get really exhausted right before and during the first day of my period. It's not fun, but it's not that uncommon. If it continues to be a problem for you, you can talk to your doctor. Extreme fatigue around your menstrual cycle can also be a sign of a treatable condition (like low iron, or a simple thyroid issue).