Ovulation after miscarriage

I had a missed miscarriage on Feb 1st. The Dr advised to do a pregnancy test at 3 weeks post miscarriage to check everything had passed. I took one yesterday (at 2 weeks and 2days after) and it was still a blazing positive. After such a crappy 2 weeks, lastnight me and my husband had a meal out and enjoyed time with each other. It just seemed right to be intimate and yes we did have sex. Obviously now I'm worried that there's a possibility we may have conceived (not a bad thing) but because we didn't get our negative test, it could confuse things. Would the hospital scan me if the test is still positive? Would that pick up a new pregnancy? Is there even a possibility I could have ovulated 16 days after miscarriage if the hsg test is so clearly positive?