This question already has an answer here:
This one has always bothered me.
Is this sentence correct?
He shivered, thinking about his and Anya’s first time in the hospital.
It feels awkward, but there's a need to refer to their shared experience.
This would also apply to something like:
I shivered, thinking about mine and Anya's first time in the hospital.
Again, it clunks, but I can't see an alternative.