Doubts about the gestational age of the baby based on a first sonogram

Patient : I went for my first sonogram today and since I could not remember the date of my last period, the tech had to go off an estimate based on the size of the baby. She estimated 22 weeks, so I would have conceived around Feb 4, which does not make sense. After the test, I am remembering when my last period ended and it ended around Feb 12. Less than a week after that, I had unprotected sex with the father twice within 2 weeks and took plan b both times within 72 hours (24 hours the first time) I missed my period the next month so I took two home pregnancy tests on March 22, which would have been a little over a week after my missed period, and they both came up negative. So based on all of that, the tech's estimate was way off, more than a month. Is that normal? I thought that plan B was 95% effective if taken 24 hours after unprotected sex and home pregnancy tests are 99% accurate, so I don't see how I could have conceived at the beginning of February. I feel very uneasy about this whole thing and could use some information about what could have happened and if its possible the tech could have been off this much when estimating the date of conception/due date.
Doctor :   The 3 basic methods used to help estimate gestational age (GA) are menstrual history, clinical examination, and ultrason ography. Clinical signs are highly non-specific and subject to error. In the absence of information regarding the last menstrual period, date of positive pregnancy test; ultrasound examination is the only reliable way of estimating the child's gestational age (GA). Fetal biometry by ultrasound in the second trimester (from 12 to approximately 22 weeks of amenorrhea) can yield acceptably accurate estimates of the age of the fetus. The best parameters are the biparietal diameter (BPD) and the head circumference (HC), which correlate well to GA. GA estimates by the BPD or HC have an error range of plus or minus 8 days If the first scan is done after 22 weeks, its accuracy for GA assignment is reduced considerably, and estimates may have confidence intervals of plus or minus 3 weeks. While interpreting these results, remember that the gestational age is counted from the estimated last menstrual period and is not same as the clinical age of the fetus. The clinical age is counted from the day of conception i.e. the day of fruitful intercourse and is actually a more accurate parameter of the age of the fetus.

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