Does anybody else struggle really bad with black-and-white thinking regarding rare but bad events?

Example: I have pretty severe insectophobia. Several months ago, a spider made its way into my teacup (and died, because boiling hot water, lol) while I was making tea. Thank god I saw it and promptly dumped the tea before I drank any of it, but it freaked me the fuck out and now every single time I make a cup of tea, I obsessively check at it to make sure there aren't any spiders, and I also have to move the mug to a different location in the kitchen so future spiders "can't find it", which is complete crazy person behavior.

The spider getting into my teacup was a chance occurrence. It has happened once in my life and probably won't again for a long while. But my brain sees this single bad thing happening, rips itself into overdrive, and goes "THIS IS THE BEGINNING OF A NEW PATTERN. THIS BAD THING **WILL** HAPPEN VERY OFTEN FROM NOW ON. BE PREPARED. ALWAYS ANTICIPATE IT. ALWAYS THINK ABOUT IT."

Writing this feels very embarrassing and like "it's not a big deal, why are you having a meltdown over this when it's not even that bad", but that's just the Disorder part of anxiety disorder, huh? It's not always with super mundane stuff like the occasional household pest, it happens with bigger deal things like bad interactions with certain people, and crossing certain streets.

I have suspected for a while that I have OCD on top of having anxiety. It's like I don't know how to stand back and convince myself that rare occurrences are rare because all I can do is interpret it as a new, guaranteed pattern, which I must then guard myself from to prevent further discomfort.