I am so confused! help!

Jessica
Has anyone conceived after there expected missed period? If that makes sense or even possible lol 
Long story short, my lmp was Jan 3rd. Was suppose to get my period Jan 31st but didn't. My period is always on time and I use an app to track it. Well after 13 days late, I got a positive test after having 2 negatives. I also got very light pink spotting on Feb 13th. Went to the doctors and he didn't do a urine test because according to him "if you have a positive home test, then your prego." Had blood work done 4 days ago (still haven't heard back) and scheduled an ultrasound for this past Thursday. Well I went for the ultrasound and she said it looks like I am only 4-5 weeks as she could only see the changes to uterus and possibly a small sack but it was hard to tell.
If this is the case and if I am only 4 weeks, then I would of had to conceive the first week of February which doesn't make sense to me if I was suppose to get my period Jan 31st..Or maybe I am calculating it wrong but I used an online calculator to try and see when I would have conceived and that's what it's saying :/