Had an ultra sound today now I am confused

So I had an ultra sound today to find out how far along I am because I just had a baby January 18th the ultra sound said I am 6weeks 5 days and a due date of December 16th so when I did the math it means my date of conception was march 25, but I tested march 31 at night time also so it wasn't my first morning pee I got a super faint line. I feel like the ultra sound might have been wrong. It wasn't done at my drs office it was done at a free clinic that helps you before you get to go to your drs. What's everyone opinion do you think it could have shown up 6 days after conception??