Sure.
In general, having sex on day 2 or 3 of your period (I assume you were even still bleeding, if your period arrived on August 1) is too early to produce a pregnancy because you wouldn't be ovulating yet. Sperm can live in your system about 4-6 days, but you would still have to ovulate awfully early compared to when your period came for even August 3 to give you a pregnancy. Sometimes a woman can ovulate on day 8 of her menstrual month (using a count beginning on the first day of her last period), but it's not that common.
The August 7 or August 13 sex is much more likely to have produced the pregnancy.
When did you find out you were pregnant, and was it by a home test?