Jeanne, I had a similar experience on my first certification dive- a beach dive in rather choppy conditions. The BC that I was in was a child's BC but the instructor had put 16 lbs on my weight belt. I started struggling to stay afloat on the way out &, like you, never thought to drop my weight belt. Luckily a friend was along for the dive & noticed my struggles- the instructor wasn't paying any attention to me. (he was too busy playing with his GF who had come along on the dive). I wound up handing off my weigh belt & doing my surface skills without it. Then, I put it back on to do the actual dive (&, yes, my instructor spent the dive playing footsie with his GF). Needless to say, I had some very harsh words to share with the shop owner when I got back but the bottom line is that I came back safely & learned a valuable lesson early on about the options that I had. Like you, I did not think to drop my belt or put my reg in my mouth & go down (10-15 ft of water) & come back to shore.
VERY glad you made it back safely! :fruit: Here's hoping that your story & mine might make a difference to someone reading this thread.