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context:
I twisted my ankle in talent rehearsal. I do rhythmic gymnastics, which is, like, really cool. Nobody else does it. And I tripped over my ribbon. And I didn't get stuck with someone this clueless, and that was, like, a nurse.

thanks a lot.
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In the given context, "get stuck with" means "be placed in an awkward social situation where you have to try to be nice even though you find the other person(s) totally boring, unpleasant, unattractive, or incompetent".

When you get on a plane by yourself, you usually hope you won't get stuck sitting next to someone unpleasant.

When you are shown to your seat in a theatre, you most likely hope that you won't get stuck sitting next to someone who is constantly fussing with candy wrappers and giggling with friends.

In dance class, when the teacher assigns partners, you hope you won't get stuck with the least attractive partner in the whole class.

In physics lab, you hope you won't get stuck with a lab partner who is all thumbs.

CJ
Comments  
excellent!
thank you ever so much!