Thanks for the image. I'm going to rework all the calculations and explain once more what the possible range of conception is so that we can be as clear as possible.
August 29th 1st trimester u/s = 7w4d
That makes the most likely conception day 5w4d earlier. That date is July 21. Yesterday I used a "wheel" so was off by 1 day. Today I counted back day by day.
The error range on a first trimester ultrasound is plus or minus 3 days. With older machines it's 5 days. The error range is written on the final report. Because of the geographic location you live, I think 3 day range is more likely than 5. So I'll use 3. The reason for the error range is that the measurement is somewhat technician dependent. The technician needs to get the best side view possible. Sometimes the correct angle can be difficult to get. Also the technician needs to place a small caliper mark on the edges of the embryo. This caliper mark has a certain width too.
With a 3 day + or - range added, the range for possible conception dates is July 18th to 24th. If 5 days + or - range is added, it's July 16th to 26th.
Sperm can live for up to 7 days inside a woman so we need to add that to the front of the range which gives us July 11th-24th or July 9th-26th.
You say the sex was on the 28th. That is technically outside the ultrasound determined range, but it's just 2 days off which is actually quite little. If the technician was a bit sloppy, that would be enough to throw it off by that much. The image you sent is certainly not the best side view for measuring but also I don't see caliper marks on the image so the technician probably didn't give you one of the better images.
If you have other reasons to suspect that she was unfaithful, then do go ahead and request a paternity test. This can be done using her blood and either blood or a swab from your cheek. But tread carefully. This can be a relationship changing accusation. If you want a paternity test, be sure to use a company approved legally in your state. In most states, that information can be found on your states website using "paternity testing" in the search engine.
This is a tough situation. I wish it was clearer one way or the other. But the numbers are just quite too tight. If she has another ultrasound, it should be done in about 2 weeks. The larger embryo size would reduce some of the technician error but still be in the range where the growth of the embryo is very consistent without variation of genetics and environment influencing the growth yet.
I hope this was clear and helpful. Let me know if I can add more details.