Hi, during an excessive exercise like the running long-distance may result in such symptoms, if done with under preparation and practice. As your daughter was sick and having cold and maybe she was under prepared and under practised as well, this could be the main reason. Lack of proper hydration in the body will ultimately lead to lack of circulatory volume and therefore less oxygen carrying capacity. So the reason is both. I hope this helps.
wow, the pupils I don't know but if she wasn't sweating: I hope you took her to a doctor. That is one of the first signs of heat stroke. If this happens often at all you need to worry, heat stroke (unlike heat exhaustion) can atually kill a person becuase it messes with the hypathalmes (aka body heat control central). But because you said she was cold and numb, she could have been in the late stages of heat exhaustion so you caught it in the transtion. Make sure she's drinking plenty of water all day before meets. I'm a cross country runner myself and it's very very important. If she can have her drink two to three water bottles full a day before running (if she does in the afternoon).
But oxygen deprived is mostly not it. Just tired and a little out of shape. Awseome that she's doing cross country. I'm not a runner at all, but I'm guessing she's great at it. Tell her to keep up the work!
Most likely a bit of both. If she was sick and wasn't running for a week or so before she may be just really tired. Also cold meda can dehydrate you so make sure she drinks lots of water. Also getting back in shape after being sick can an will take time. I was dead sick asleep for 4 days and it took about a week before I was back to full ability.