Is it possible for me to be pregnant if I had my period a week after unprotected sex?
You are essentially asking if you can get your period while you are pregnant, and the answer is no. A typical period is a sign that you are not pregnant. While there are some variations in bleeding that can happen in early pregnancy (light bleeding or spotting that doesn’t last for more than a day or two, does not fill a pad or tampon), experiencing a full period is not one of them. A full period is shedding of the lining of the inner wall of the uterus, and this will only happen if implantation of a fertilized egg has NOT occurred.
Based on your description, it sounds like you had sex about a week before your period. At that point, you had likely passed your fertility window and the chance of pregnancy is essentially zero. The fertility window is about 5 days before to about 24 hours after ovulation. Ovulation occurs mid-menstrual cycle, usually about 14 days before your period.
If you’re wondering if you’re pregnant, take a pregnancy test. But based on the timeline in your question I would guess that there is no chance of pregnancy.