Alison: I would advise checking with a doctor first as she could have an eye infection, in which case they may prescribe a form of antibiotics for her.
If she's looking for something gentle to wipe over the eye area in the morning, I'd definitely suggest Liz Earle Eye Bright which contains echinacea extract. She could apply this with clean cotton wool, just by wiping over the eyes. Most importantly though, a separate cotton pad must be used for each eye to avoid spreading infection, if there is one, from one eye to the other.
If she's rubbing her eyes throughout the day, she should be aware that she could cross-contaminate them just with her fingers or even a tissue or hanky. The same applies to items like a mascara wand or eye pencil. So, if she does find she has an infection, she needs to throw away any eye make-up as this will be contaminated too.
If she does wear make-up, make sure that she's removing it each night as forgetting to do so can result in sore or swollen eyes the next morning. She needs to be using a proper eye make-up remover too, like the Gatineau Floracil Eye Make-up Remover.
In terms of using a moisturiser around her mouth and eye area, I'd recommend L'Occitane shea butter because I'm concerned about sensitivity. It just needs to be warmed between the fingers and then massaged around the mouth and eye area. Shea butter is particularly good for her as a lot of moisturisers we do are concerned with tackling ageing skin, which she just doesn't need at her age.