Here is a still.
Somewhere in these 4 books is a filter, but one would have to go page by page to find it.
First boil the water, then distill it.
Filtering through charcoal should get most of the rest.
The book adds wheat, sand, and something else, but I'm not finding it.
https://archive.org/details/KurtSaxonSurvivorVol.2/page/n53
https://archive.org/details/KurtSaxonSurvivorVol.2/page/n95

Bathing is almost as bad as drinking, so I hope you got fire to boil plenty of water.