Sure, your fiance's sperm could have lasted "that long," and besides, you don't know when you ovulated. Counting out 14 days after a period is not proof of anything. I assume you know that ovulation is the starting event, and the period is the ending event, in an ovulatory cycle? (The period doesn't lead to ovulation, ovulation leads to the next period.) Your brain gives a signal and your body ovulates, then about 14-15 days after ovulation, if you haven't gotten pregnant a period comes and erases the uterine lining because it wasn't needed. After that, your body ovulates again whenever it feels like doing so, which could be lots later than 14 days after the last period. So, #1 point is, when your period came doesn't say much about when your next ovulation was.
#2 point is, you made a guy with a proven vasectomy take a paternity test? Why? If the answer is, "I think the guy was lying and faked his lab test and he really didn't even have a vasectomy," I guess that is understandable. (It does raise the question, why would you sleep with that guy?) But, if the answer is "I don't trust medical science and vasectomies are so terribly complex and difficult that probably his failed and the fact that his lab test later confirmed 0% sperm is likely a mistake," well, my dear, getting a discreet DNA test with your boyfriend will probably not solve your worried mind, because you won't believe that test either.
I'm kind of teasing you but not quite. And believe me, you are not the only woman who has ever written on this site who had sex with a guy with a vasectomy behind her regular guy's back, and then out of guilt and fear not only made the sneak-around guy go get his vasectomy tested with a sperm count, but then pushed the poor dumb jerk (who doubtless by then was sorry he ever slept with her) into also getting a DNA test, because, you know, so what about the vasectomy. I'm here to say, don't ruin your pregnancy by stressing with made-up fears. You slept with a guy who had a VASECTOMY. A later test proved he has ZERO SPERM COUNT. Let those facts soak in. :-)
#3 point is, when you did test with Mr. Vas, to nobody's surprise except apparently your nervous brain's, he is not the dad. He is SO not the dad. He has 0% possibility of being the dad. This is not a test of his vasectomy, it was a test of the DNA of your child. It was not a match. This means one test, the sperm count test, said he can't produce children. And a totally different test that tests something totally different, DNA, said he didn't produce your child. One test backed up the other. Let that soak in too.
Now, regarding a discreet test. Yes, you could do one with your partner's toothbrush. My recommendation is, only do it if you are going to finally believe this test. But remember please that you have so far pooh-poohed a vasectomy, a confirming sperm-count test of the vasectomy, and a DNA test. What will make your reaction to this test different?
In your shoes, I'd work with a therapist or counselor and try to get to the causes of your anxiety. I can promise you that it's not "who is the dad?" because if it was, you would have taken the tests already done as proof, and been glad to have them. Something probably more hard to solve is likely behind the fact that you are still stressing. If you're interested, I can give you a list I often post of reasons women won't believe the black-and-white test results that they are reading with their own eyes. These worries are often in the areas of survival, conflict in one's internal belief systems, or relationship dynamics. You might dig into some of those with a counselor, and if you do, you'll probably see the irrational fear about paternity will fade away. There's little enough point in spending two thousand dollars on a test that gives an answer to a problem that deep down is not what is worrying you.
Good luck, sweetheart. I just want you to know that women have written in saying they ruined what could have been a perfectly nice pregnancy stewing over worries that weren't realistic. Address real concerns, and the fake worries tend to drop away.