Get your own room. Barring that, push the cot as far from the AC as possible, or sleep on the floor.
Would you be comfortable bunking with Mom and letting Sis take the cot? I know some people are uncomfortable sleeping in the bed with others (I am depending on who it is...I could sack out with my MIL, but not my SMIL, and I sleep with close friends on occasion....hmmm, that sounded really abd-minds out of the gutter folks!!) but if neither one of you minds it it might be a better solution.
I can sleep and prefer to sleep in the cold. But too much heat and my nose dries out like a little raisin and my sinuses dry up and ache all day.