Why would a random position from your game appear in a puzzle database?
Perhaps because one of your positions appears puzzle-like to you? Why not post it here?
That is the exact moment for you to spend some time looking deeply into a position.
As far as setting up a separate database where one could compare any position to any known position in the universe of stored games, that's what paid databases have done for years. They typically charge a fairly hefty fee for that service.
However, you just want to look at a smaller database-- the universe of stored puzzles on Chess.com. Let's guess that Chess.com has a million puzzles in its database of puzzles.
There are tens of billions of games played every year. There are probably a few hundred duplicates every day but I doubt if it is a big percentages of all the hundreds of billions of posiitions beyond move 15 or 20.
Appreciate it