Well, sex on the same day is impossible to sort out without a DNA test. How do you know that eventful day was the day that produced your pregnancy? What if you were pregnant from your boyfriend already before you had the sex with the ex?
If you know FOR SURE that this is the only day you had sex in months and you are now pregnant and it cannot be any other possible day, here's some stuff to know.
'Pulling out' is not a method of birth control, it's just a justification. If sperm was in his urethra from an earlier ejaculation, it could ride into your body in the pre-ejaculatory fluid and the guy would not have to ejaculate during the sex to expose you to sperm.
The "short sperm count" stuff is also b.s. One single ejaculation contains millions of sperm. Even a tenth of that amount that is still many times the amount needed for you to get pregnant. Unless your boyfriend has given you lab results from a doctor that shows he has 0% sperm count, you can't believe anything he says. Just like the guy who pulls out, it sounds like he just didn't want to have to wear a condom. Where did you get these guys? Don't they care about you at all?
DNA tests for paternity are available both before the baby is born and after the baby comes. Only those done after the baby comes (by a lab approved by the family courts) are legally admissible for child-support purposes. But if you are desperate to know beforehand, you could contact either Ravgen or the DDC. You will find that their top-quality prenatal testing is about ten times as expensive as DNA tests done after the baby comes. (Don't bother with so-called DNA labs that advertise heavily on the Internet. Those are simply a waste of your money). Sometimes the woman and both men share the cost of prenatal testing 1/3- 1/3- 1/3, but they have to be on pretty good terms to do that, I think. Often the women who write in here for advice can't afford the prenatal testing and so it is a moot point.
When you do post-natal DNA testing, talk to your doctor and/or call the clerk of the family courts in your area of jurisdiction, and find out an approved lab for this kind of work. Don't do a drugstore test, courts don't find them reliable because of the risk of fraud or mis-handling of the samples. Go to a lawyer if the guys won't test. They pretty much have to, if you are filing for child support. Test with both men, of course, and go with them when they do it so you can affirm it is really them.
Sorry you are in this mess. Write back if you think there is a chance you got pregnant on a different day. What you could be doing is called the "flashlight effect" -- because this dramatic thing happened, you are assuming it caused something. Maybe it didn't. Write back with more detail if you want to check the dates.
OK, well, it doesn't sound like you got pregnant on that particular day if it was 6 weeks 3 days back from when the doctor said you were 6 weeks 3 days along. I'll tell you why this would be so, but please first tell me, did the doctor say this after looking at an ultrasound? Or did the doc simply look at a little cardboard wheel or a calendar and ask you the first day of your last period and no ultrasound was done?