This is going to be the last day or so of her period....meaning light and stopping flow.
As b-fly said, the counserlors will surely have a stockpile of them.
However, there is the concern if they give her some, and she uses them, the aunt, who sounds like the caregiver, could be really pissed off.
If I had a daughter of 13, who wanted to use them, but I didn't want her to use tampons yet, or at all, I'd be livid if an adult gave her one and showed her how to insert it.
I'm just sayin'
It's different if another girl did it. I might be mad, but hey, they're peers. Whattaya gonna do, huh?
In any event, I don't know that going away to camp would be the best time to start using tampons anyway.
There is an art to figuring out how long your body needs to have it changed, and if the flow is heavy you usually use a pad in addition anyway, for accidents.