Are you on town/city water? Then relax because it is tested and treated regularly. You can call your town's Department of Public Works or the Health Department to get a copy of the water report - it's probably on line. That would be much more productive and accurate than scaring yourself to death with endless Google searches.
Are you on well water? Have you had it tested?
What symptoms does your child display? None? That's what I would expect. The chances of there being a problem are less than being struck by lightning. Do you keep your kids inside so that doesn't happen? Or do you trust that it's so unlikely that it's not worth worrying about?
You are in California, according to your profile. The very few cases that occurred were in Louisiana, and while the causes are unclear, there is some speculation that damage to the water supply still left over from Hurricane Katrina was a factor. (If that concerns you, then write to federal officials and demand that they go in and finish the clean-up from Katrina now that 10 years have elapsed). There was also concern about insufficient chlorination in Louisiana, but again, the water report will calm your fears on that. Given California's water situation, I'm pretty sure that official agencies are on top of safeguarding the water supply.
There are bacteria and germs all around us. We all have to let our kids swim, play, go to school, eat, and be normal. In fact, the more you let your kids be exposed to things in small doses, the more they are going to develop strong immune systems.
I think the best thing to treat is not your child, but your panic issues. And I know that nothing we can say here will calm your fears even if they are irrational and baseless because they feel totally real to you.
All our kids have played with sprinklers and hoses, my little dog used to "attack" sprinkler systems and get water up her nose and down her throat, we've all gone swimming in lakes where these amoebas occur in minute quantities, we've all had our kids playing in dirt and sandboxes, and all our kids are fine.
I hope you get good results from your meds. In the meantime, call your child's pediatrician and ask for a list of symptoms and any info on amoebas in your part of the country and what symptoms to watch for. But right now I think the greatest risk to your children is a mom who is numb and crying all the time - you are so focused on this minute possibility that you are a much greater danger to them if you are driving them in a car while distracted or using a stove while unfocused. And no kid benefits from having a panicked mom all that time - so please focus on yourself and get the help that you need to be able to function in a balanced and calmer way. As they say on the airplanes, put the oxygen mask on yourself first, and then attend to your child.