I'm no expert, but I think you might want to have a look at Standard Methods for the Examination of Water and Wastewater. As you might gather from the title, it is the authoritative work on the subject.

Based on my limited experience with water testing, I think you might have better luck using filtration to concentrate samples and culture techniques to demonstrate presence or absence of possible pathogenic organisms. As much as I hate to say it in this crowd, a microscope may not be necessary for the task you have in mind.

That said, it seems to me that you have not established cause and effect between your pool and your illness. I have had two or three bouts of Montezuma's Revenge over the past many decades, and I can't even remember the last time I was in a swimming pool. I think if you just treat the pool according prescribed procedure, you should be just fine.

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John Karlsson
Hope Valley, RI

Don't count your chickens until they have burned their bridges behind them.