Water would be tested at the potable water pumps, not the lake itself.
Sounds like it could be e coli, but there are a lot of microbes out there (giardia).
If this was my child, I'd take him to the ER (or, at the very least, call our doctor). These things can turn bad quickly.
By the way, at age 18 months, you CAN "be staring at her every second" when you are around water. If you had been, you wouldn't be worried about her drinking the lake water.
I hope she feels better soon and that it is nothing more than something minor and short-lived.