Funny enough, I heard that was one of the origins of Spider-Ham, he was a spider bitten by a radioatice pig (a mad scientist pig-woman that later would become his "aunt" May since the radiation accident gives her amnesia)

Technically girls (and boys, and potatoes) are naturally radioactive as they contain a small amount of radioactive isotopes occurring naturally. When I slept on a regular radioactive couch after eating a regular radioactive potato I became the hero known as Couch Potato!

If we're going with a new origin, how about a squirrel who ate the Human-Human Fruit?

There was a character in the comics called "Girl Squirrel" who might have claimed this origin, but she turned out to be something else. Ah, well.

Do Italian Spiderman next!

Reminds me of the backstory for "The Crimson Chin" who was bit in his chin by a radioactive handsome actor which gave him amazing chintastic powers and a amazing chintastic costume, also his chin became about half a metre to a metre long.

Squirrel Girl was a mutant, until Disney had issues with Fox, but rather than make her an Inhuman, decided it better fit her character to say she was just born how she is but doesn't have an X gene or inhuman gene or alien genes. So fan theories can go crazy about her origins all they want.

that radiactive girl went on a bite spree

Squirrel Girl is a legally distinct mutant. Not a Mutant, just a mutant. Born that way.

Would.

"Girl power" - Tits and the ability to entice lonely nerds with sex appeal

I thought (and she thought for years) that she was a mutant but the wiki says she's not "She suffered a modification in her genes for unknown reasons". No further info. Kinda annoying.

Actually this is closer to Spider-Ham's origin then Squirrel Girl.
A nice ordinary everyday Spider that gets bitten by a Radioactive Pig.

The ability to control a dog through mere vocalizations seems like an ability a squirrel might want, and girls often have that power.

Human-level intelligence, massive size (for a squirrel), and opposable thumbs all seem like powers a squirrel might hope to gain from being bitten by a radioactive girl.

In fairness, this is basically Spider-Pig's origin: it was a spider bitten by a pig, not the other way around.

pretty unusual for a squirrel to rest on a carrot