Technically women have found out as early as 15 weeks before but it all depends on what your doctor is willing to do. I had an appointment when I was 15 weeks and 3 days and asked my doc if we could find out the gender but she said to just wait to my 19 week appointment.
So if you aren't scheduled to get an ultrasound next week I wouldn't get your hopes up too high. And even if you do get an ultrasound there's a good possibility it could be wrong because some babies are still developing their private parts at 16 weeks whereas some babies are developed enough to show.
With my boys I was told around 15- 16 weeks. With my girl I was told at about 15 weeks also. I all depends on the on the accuracy of the ultrasound and if your doctor is comfortable telling you at that point. It definitely is possible though! Good luck!