I’d say that’s a specialized form of the usage that eburacum45 alluded to: the noun “get” can be a (rather archaic) term for “offspring.”
Anne McCaffrey wrote a long series of books about the Dragonriders of Pern. One of her short story collections was to be titled Get of the Unicorn, with Get meaning offspring, from beget.
Nobody at the publisher remembered the obsolete term, and the book was published as the seemingly more logical Get Off the Unicorn.
Reason #1,333,309 why writers hate publishers.
I’m still laughing at that. Thanks!
In my dialect, I might say something like:
“Whenever I’ve eaten warm oysters, I’ve gotten sick.”
Is there a form of “get” that you’d use in that sentence, or would you need to use a different word altogether?
Same here. Chicago. “Got” to mean "have’ is a pretty normal colloquial usage. “Aw, shit, I only got ten bucks on me.” “I got some news for you.” “Whatcha got?” “Got any more beer?” “Got milk?” 
Sometimes I’ll sneak the have or 've into it. Sometimes not. Sounds perfectly normal in my dialect, if not considered non-standard. My grammar school English teacher would not be happy, but I don’t care.
It was 1977, so just an old-fashioned, numb-brain fuck-up.
She was trying to teach formal written English, because that’s what schools do. Spoken English, as every linguist knows, is a whole 'nother thing. I hope she knew the difference, but it’s possible she was brainwashed by the early century prescriptivist movement in her own schooling.
Henry Watson Fowler wrote A Dictionary of Modern English Usage in 1926, a 750-page, small print style guide that overwhelmed the competition. It went through a million reprintings, and was later adapted for American usage. People would just refer you to Fowler to settle any argument on how to write good. Interestingly, some of the purist idiocies - like never ending a sentence with a preposition - he called superstition, but somehow the prescriptivists just looked at what he said not to do and ignored the stuff he allowed. This attitude poisoned generations of schoolkids.
Full disclosure: I was taught to be a prescriptivist and had to learn to otherwise as an adult.
Archaic. I’m pretty sure that’s not part of any modern UK dialect (certainly not mine).
This begs for a Winston Churchill quote, who, when criticised for ending a sentence with a preposition, supposedly replied: “This is the type of errant pedantry up with which I will not put.”
Might not be Churchill, lots of anecdotes are falsely attributed to him. But still nice.
I’m pretty sure she thought we were lesser human beings for using improper grammar. That’s how about 2/3 of my grammar school teachers were. Very old school; some were nuns.
Don’t they have ‘speak like a pirate day’ round your way?
“Whenever I’ve eaten warm oysters, I’ve gotten sick.”
“Whenever I’ve eaten warm oysters, I got sick.”
Personally. I would just say: “Warm oysters make me sick.”
But you’ve changed the meaning.
“Whenever I’ve eaten warm oysters, I’ve gotten sick.” May imply coincidence.
“Warm oysters make me sick.”
Shows cause and effect.