How accurate are ultrasounds???? HELP

So I went to the doctor for the first time ever for my baby. I went in thinking I was 6 weeks from exact day of conception which I thought was March 13th. The doctor told me I was little over 9 weeks & 3 days from the measurements she got thru the ultrasound. My concern is if I count back from today’s date. Which I also did w doctors. She says the baby timeframe I would’ve gotten pregnant would be March 3rd. March 3rd was the last day of my period, February 25th would’ve been my first day. My first question can you ovulate while being on the last day of your period ? Also my concern is I’m w my baby daddy I started started talking to him Feb 17th & have only been w him since we started talking. Last time I was w anyone else was February 14th. I don’t want to go thru this pregnancy thinking of the chances it is to be someone else’s baby & not his, especially since I already told him it was his. My question is how accurate are the measurements on ultrasounds ? And the dates when it comes to weeks old ? & with the dates I’ve told you ladies ? Do you believe I’m making the right decision by saying it’s my baby daddies ? Please take your time looking at the dates again? I’ve been scared and crying none stop. Last time w someone else Feb 14. Last period February 25th thru March 3rd. Doctors says I’m 9wks3days.