I see every reason to believe your daughter belongs to your boyfriend. You should quit hunting the Internet for reasons to believe otherwise. Please enjoy the rest of your pregnancy, your new family and the years to come.
They weren't saying you should go back and change your estimation of when the baby was conceived, they were saying your baby was developing slightly faster than average in his or her early weeks. But even if you needed to set your perceived conception date back a week, that wouldn't explain an ultrasound in your fourth week seeing nothing. (Nothing is nothing. If you were really in your fifth week, it would have seen something.) And the following week, it would have seen a lot (limbs and movement) if the baby was really 6 weeks GA instead of 5.
You're saying you had a period a week and a day after the last sexual activity with the guy who is not your boyfriend. I assume you're aware that people don't ovulate a week and a day before their period? So you wouldn't have gotten pregnant from the sex on the 16th in any case. You also say it was a normal 5-day period and came when it was supposed to, and your ultrasounds all say you conceived in March.
The only puzzling part in your story is what is driving you to freak out. I assume you realize that stories on the Internet are not vetted by God allowed to stand only if they are the pure and honest truth.
In regard to the doctor having a sensitive test, I'm not finding that very unusual, either. When I was pregnant, I got a positive blood test on day 8 after sex, and on a home test, eleven days after the sex.
My suggestion is that it's neither the Internet tall tales nor the early positive pregnancy test that's bothering you, but something else about your situation. It might be a good idea to address that, and if you do, your worries about dates will fade away.