Sorry you’re having such bad experiences. As others have indicated, as long as you’re using the same size battery (AA, AAA, whatever), the Volts and other specifications would be exactly the same, in the USA or Europe.
You mentioned your car key fob - is that a remote lock/unlock device, and maybe is even needed to start the car? Is this your car, or a rental? I’m guessing the fob uses a “camera” type battery, a disc, like a thick coin. If you’re replacing it, of course, make sure the code number of your replacement matches the number stamped on one side of the old battery, I hope the electric gremlins don’t pester you further.
A side note: for years, Rick Steves has said if you run out of toothpaste in Europe, head into a pharmacy. That’ll give you the chance to pick up something you think might be toothpaste. He doesn’t mention electric toothbrushes, which would be a considerably costlier adventure. I’ve traveled for years with a German, manual Fuchs-brand toothbrush, and they’re well naw.