Is it possible?

Michaela
Ok so my last period was September 24th and I took a test on the 19 and it was negative, then I took one on the 25th and it was positive, now if I conceived the week after my period then that would put me at being 6 weeks and 2 days right. But I went in for a ultrasound and they did see anything not even a sack. Now I know that it takes 6 to 12-days to get a positive pregnancy test but if that was true then I should have gotten a positive on the 19th because that would put it close to being 12 days but. My first hcg level was taken on the 29th 4 days after I took a test and was positive but very faint. Any ways it was a 87 Now we did have intercourse on the 13th 2 time and on the 15th which would put me at being a week and 6 days when I found out. So is it possible for me to be only 3 weeks and 3 days do you think I could have conceived on the 13 th or 15th?