Our community leader has fully answered your question. We wish you well.
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The count of a pregnancy in "weeks" (gestational age, or GA) was developed before ultrasounds. It uses as its start point, the first day of the woman's last period before she got pregnant. The GA count begins when she's not even pregnant yet. Pregnancy from conception to full-term birth is only 38 weeks long, but all GA measures use a 40-week count, in order to start at day 1 of the prior period, which the count assumes to be two weeks before conception. All medical textbooks, doctors, nurses, "What to Expect When You're Expecting", ultrasounds, everything medical -- count out the pregnancy time period that way, with two weeks where you are actually not pregnant added at the front end. The day you were told you were "6 weeks 2 days pregnant" by a doctor or ultrasound tech, if you had said "Do you mean that I conceived 6 weeks 2 days ago?" they would have said no. If you were told from an ultrasound that you are 6 weeks 2 days GA, that means you are 4 weeks 2 days from the day you conceived.
If you knew all that and were just freaking out, please think again. If you had gotten pregnant from the sex on July 12, the ultrasound September 13th would have shown that you were in your 9 week. And the earlier ultrasound would have shown you to be in your 7th week, which is a very visible embryo, not a small possible gestational sac where you had to go back later to see if it was a pregnancy.