It's impossible to fully just shut off your fears, but I do think there are a couple of things you can do just generally to help yourself.
In this specific instance, there's no way you're going to get an amoeba from fresh tap water. I'm sorry, it's just not going to happen.
But beyond that, you'd do wise to try and avoid google and/or looking up health-related info online (I'm sure you know this already), and to also cut back on the reassurance-seeking behaviors (yes, even coming on here and asking for help). While both of those things might feel good "in the moment," ultimately they're holding you back from true recovery and they're not giving your nervous system a true chance to heal.
You sound a lot like me, saying that you KNOW you're being irrational and yet you can't help but be concerned. I totally get it, and when my health anxiety was bad, I was just like that, too. So to just say to you, "well just don't google and don't ask for reassurance," is not only cold comfort, but let's be honest, you're still going to do it anyway, most likely. The fact that you have this awareness is good; it's a first step. You could go on like this for months yet, in full awareness that what you're doing is counterproductive. It's not until you truly WANT to stop feeling scared about your health that you'll actually and fully curb these behaviors.
Whatever that switch is for you, I've found that you can't really force it from happening. In the meantime, I'd try everything in my power to curb the reassurance seeking behaviors (and if you can't, just be aware that they're what's keeping you trapped in this cycle), and seek some professional treatment (or at least some serious self help work). With both of those things, eventually you're going to find your mind clearing.