A single seminal ejaculation produces something like 100 million sperm; two weeks abstinence does not change sperm motility overall since there are so many. Even someone who does not regularly masturbate can have a wet dream. I would challenge the statement that someone is not "the type" to masturbate.
Here is the thing about the testing.
Prenatal paternity testing used to be done only when there was another medical reason to do a procedure, which were, CVS or amniocentesis. A doctor would not order one of those procedures merely to find out who the father was, but a DNA test could be done in conjunction if there was an important reason to do CVS or an amnio (and finding out who the dad is, was not considered important.) Some women today do not know that prenatal DNA testing for paternity can be done without any invasive procedure. Today's DNA testing, if done before the baby is born, is done with a blood draw from the woman's arm, and either a blood draw or a cheek swab from the potential father(s). Sometimes in this forum we see women resist prenatal DNA tests because they think it means an invasive procedure, which carries some risk to the baby. Not so any more. And besides, no doctor would order a CVS or an amnio for that reason alone.
The other problem, though, is that the high cost of doing prenatal testing properly, has drawn charlatans to the field. So, even some women who might otherwise want to go ahead and test, resist testing because they have heard stories of the bad so-called labs out there who give wrong results, lose samples, or just mess up in some other way. And admittedly going to one of those labs would be a big mistake.
However, if the woman and both men test, and if they go to one of the two best labs out there for this kind of testing (which are, Ravgen and the DDC), the results are reliable. It can be worth the peace of mind for all three people, despite the high cost.
One more caveat is that once the baby is born, the courts will require a conventional DNA test (which is done with swabs from the mom, the baby, and the men) in order to have a legal determination of paternity. Prenatal testing is too new and has drawn too many charlatans to the field, for the courts to be confident in using its results for this determination. So even if the three of you did test, you'd all need to do it again when there are four of you. The good news is, post-natal tests are much cheaper.
I'm only going over this in such detail in case your friend is one of those who thinks a prenatal test carries risk to the pregnancy. It doesn't.
Good luck to you!
If I had to guess, and a guess is all it would be, I'd think she got pregnant from the sex with you on the 18th. This is because (a) not all research thinks sperm can last 7 days in the woman's reproductive tract, and (b) the research that suggests sperm can last for 7 days also suggests it is not strong and viable enough by then to penetrate the egg. If the other man from February 17 had sperm in her reproductive tract, and IF the 23rd is when she did ovulate, that would be day 6 for him, making his odds worse. Yours would still be relatively fresh.
Sex on the 25th does have a chance, since even the earliest ultrasounds (sixth and seventh week), the doctors will say +/- 1-2 days for the margin for error. That's not the +/- 7 days that they say for the twelfth week, or the +/- 3 weeks they say at the end of pregnancy, but they do concede there might be a margin. Also, the egg can last up to 36 hours waiting to be fertilized.
One thing that might add to the argument that the dad is you is if, a little later in the pregnancy, you learn the baby is a boy. The Shettles method theorizes that male-carrying sperm swim fast but die within three days, and female-carrying sperm swim slower but live twice as long. If the baby is a boy, that would suggest the sex from the 25th over any other, given that she really did ovulate around the 23rd, of course. If the baby is a girl, it doesn't mean the opposite, though. In other words, a boy suggests you, a girl doesn't give a hint either way. I don't think the Shettles method has ever been rigorously tested in a scientific study, so take it for what it is.
Did she have sex with the other person only on the 9th? Could she have had sex with anyone other than you around the 20th? It sounds like you are mistaking a GA count (gestational age) for a count that begins with conception. "Gestational age" is the 40 weeks that doctors use to count out the whole pregnancy time period, but the count begins on the first day of the woman's last menstrual period (or a computed first day, if her cycles are irregular), not at conception.
If her first ultrasound was for sure on March 27 (be sure to double-check this) and the doctor told her from the baby's measurements that she was 6 weeks 4 days then, that indicates a conception date of February 23, not February 9. If her second ultrasound was on May 4 and she was told she was 12 weeks 6 days, that points to conception on February 17, not February 3. (Twelfth-week ultrasounds are not as accurate as sixth-week ultrasounds for this kind of determination, so it isn't surprising that these numbers vary slightly.)
Pregnancy from conception to birth is 266 days long, but doctors use a count that is 280 days long with two weeks added at the front to reach back to the first day of a typical or average woman's last period. This is not because doctors think a woman is pregnant on the first day of her period, (they know she is not, she is having a period!) But it comes from the historic way of determining where a woman is in her pregnancy. In grandma's day, they did not have ultrasounds, so the only start point they did have to begin the count was the day she began bleeding when she had her most recent period. This kind of counting became ingrained and has maintained over the years, and is used by all medical personnel, by ultrasounds, by medical professors and medical textbooks. If a doctor said "6 weeks 4 days," he or she was using a GA count. This would mean that on that day, she was about 4 weeks 4 days from conception.
Obviously, what this means for you is that you could be the dad, from the sex on the 18th. If the guy from the 9th was a continuing partner, then the two of you should do a DNA test, when the baby is born if not before. But if you know for sure that you were her only partner after the 9th, it would suggest you are the most likely dad.
Why is she refusing a DNA test? There are DNA tests that can be done safely before the baby comes. They cost a boatload of money, and you have to be careful to go only to a top lab, because some of the cheaper ones out there will be glad to take your money and give you wrong results. The test is done by blood draw from the woman's arm and cheek swab from the men. If you do this, both likely dads should test, so one will get a clear "no" and the other will get a clear "yes," in other words, one test confirms the other. If she continues to refuse you, possibly you could find an ally in the other guy, who probably would like to know for sure too. If the two of you (or the three of you) could pay the cost in even shares, it would be more manageable. I would suggest Ravgen or the DDC for this kind of testing, and pretty much only if you both test.
If the cost of prenatal testing is too high, test after the baby comes, when it will only be about a tenth as expensive. You might need a lawyer's help, if she is mad enough at you. Again, this testing needs to be done with both guys. Also, it's not a bad idea to do it together, so you (and she) can see that the person there is not someone's look-alike buddy carrying his ID.
If the reason she is refusing a test is that you are pressuring her for an abortion, think again. This is her baby as much as it is from someone's sperm, and a much larger commitment, as she is going to carry it for nine months and face years of being a single mother after that. She has every right to this decision without pressure from a guy who just wanted some fun in the sack. Sorry, if this is the situation. The price of living in a time of free sexual activity beyond your grandfather's wildest dreams is that sometimes you have responsibilities.
You didn't write like you were trying to get out of it, but were trying to prepare. I would certainly be prepared, in your shoes, to find out you are the dad. If she kept on with her other partner, you only have a 50/50 chance, but be ready.
Good luck!
Annie