You searched where you thought the waterline was? Wow. How deep did you dig?
There are a lot of people on TN that have been searching the Treasure Coast for years and there is a very good site to get helpful hints
http://treasurebeachesreport.blogspot.com/ Where ever the old waterline is, believe me, unless recently lost, dense silver and gold is under many feet of sand especially in the dunes. Add beach restoration on top of that. But the sands are always shifting. Pottery will move with the waves. So my point is thats its very hard to find old heavy metals unless we have a storm.. Preferably a hurricane to strip the beach sand. I guess its not impossible but highly unlikely to find old heavy metal in deep beach sands. I maybe could give you more information if I knew your area.
Your find is most likely a fire nugget. You would be surprised how heavy melted aluminum will feel in your hand. If yours is very light, it could even be a melted foil pack. We all have buckets of fire nuggets. We even have a Fire Nugget Club here at TN. Im not sure what exactly they do.

I guess they get
together, show off their finds and refute silver testing methods.
In the slim possibility that its melted silver, you should have it tested. But please have it tested by someone knowlegable on silver testing.
I would love to see pictures of the petrified wood. I found a piece myself rolling in the surf at Rio Mar..
http://www.treasurenet.com/forums/what/95456-petrified-wood-underwater.html