Your county officials offerred no guidance on boiling the tap water to kill off the amoebas? Obviously not viable for showers, but limited volumes would be sufficient for drinking, cooking, handwashing, bodywashing (with sponge or towel) .... You should inquire as to how long the water should be boiled to effectively kill off the amoebas; and confirm that the boiled water (once cooled) would be safe to use.
We weren't given any other information other than "Don't use the water." So I guess I get to do scientific research myself on a Saturday morning.
I live in a different county than Houston, but we're right on the border. Harris County doesn't seem to have our same amoeba issues, so I might have to road trip for water.