Missed miscarriage question

I went in for my very first appointment today and I am 10 weeks and four days, the doctor did an ultrasound from my stomach but couldn't really see the baby so he did a vaginal ultrasound. He said the baby stopped growing at 6 weeks and no heartbeat. He thought I might've gotten pregnant later but the thing is, I got a positive pregnancy test on the day of my missed period January 23rd...so it isn't possible I conceived later if I got my positive Jan 23rd right?? I might've worded that poorly but what I'm asking is, my husband and I had intercourse my fertile week in January, two weeks later got a positive test. We did have unprotected sex in February but it isn't possible I got pregnant from the intercourse in feb since I got my positive in January so pretty much 99 percent chance this is a missed miscarriage and not incorrect dates right? I'm schedule for a confirmation ultrasound next week just thought I'd ask...don't want to get my hopes up or anything.