What could be the thing that's smelly coming from my wisdom tooth extraction?

Dry socket : If the clot in an extraction site is lost prematurely, you get a condition known as alvear osteitis, or dry socket. Bacteria grow, food gets lodged, and it is quite painful. Keeping the area clean and not smoking helps prevent it. Pastes are placed in the empty socket for comfort.

Putrefaction: The contents of a recent tooth extraction socket is the "perfect storm" for bad smell: warmth, moisture, bacteria, and abundant fermentable organic debris, blood clot, and exuding serous exudate. Every recent extraction smells until the natural healing process allows the wound to close over, bringing resolution to the problem.