Ultrasound help!!

So I'm getting an ultrasound next week, and by then, I will have had sex 6 weeks before exactly. I'm worried it will be too early to see anything as the receptionist told me I have to be at least 5 weeks for them to detect pregnancy, and dates can be off by as much as a week. I thought I'd be okay since they count based off of LMP, but now I'm wondering. I'm on Nexplanon so I can't really base anything on a period so I just added two weeks to the day I had sex, then subtracted a week to account for the possibility of ovulation happening a week after sex. That would make me at least 7 weeks by the time of the ultrasound. Is that accurate? I haven't had a positive pregnancy test, but my mother didn't have a positive until 12 weeks with me, and 10 weeks with my brother. With him she knew she was pregnant so she got an US and sure enough she was 5 weeks pregnant. So, I figured I better make sure through ultrasound at my local Planned Parenthood.