Nervous About Finding Out Gender in a Week!!

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So, my dr likes to do the gender scan at the same time as the anatomy scan at 20 weeks. But he lets you schedule a separate appointment (at your own cost) to find out between 16 weeks and 20 weeks if you want to know earlier. I told my nurse that we have two family reunions coming up the end of June and then over the Fourh of July holiday weekend and these will be our only chances this year to see all of our family together. Since it is our first one, we want to do a surprise gender reveal at the family reunions. The nurse was super sweet and scheduled the extra ultrasound ON my 16 week appointment! I was told the dr wanted it to be between 16 and weeks and the extra would have to be after the 16 weeks. So, super excited she put the two together so it wasn't a rushed quick appointment right before we leave! Now I am nervous about it because I keep hearing so many stories of it being inaccurate at 16 weeks (or sooner) and then people find out at the 20 week or later that it was actually wrong! I was also told recently that a story of someone who found out at 24 or 26 weeks that she was actually having TWINS!!! After all the anatomy and gender scans!! 
My SIL has also been causing some stressful drama about the baby (LONG story with her!) and it has made me super stressed about if there was a mistake with the ultrasound after we tell all our families, we would NEVER hear the end of it from her! 
Any way, I am just wondering if I am just hearing the small percentage of stories out there or if I should be worried about accuracy at 16 weeks. Any one the stats or have experiences/advice/anything?