I would say to give into her this time, but actually do something to PREVENT the cramps from now on.
Sorry but I'll never understand why any woman or girl would just 'grin and bare it' or just pop painkillers in the hopes of it magically going away...unless she has something serious like Endometriosis then there's no reason why she can't prevent cramps to stop having them, or at very least ease the pain more than this.
Cell salts or clary sage oil rubbed into tummy will ease pain and help prevent them next time. Get her into yoga or some sort of gentle exercise at home, then at school show her some acupressure points to ease any cramps she may get. Or obviously at home masturbation if you're comfortable talking to her about that, or hot baths if you're not, lol.
Diet is a big deal; balanced diet with foods rich in essential fatty acids and low in refined sugars, refined carbohydrates and hydrogenated fats, avoid salty foods, and some find dairy, caffeine and soy cause problems. Get her taking omega 3, flaxseed oil (approx. 500Mg 2-4 times a day), B vitamin complex with 100mg of vitamin B6, Magnesium (100mg every 2 hours during menstruation), and vitamin E in d-alpha tocopherol form (50mg 3 times a day) - also increase calcium, iron and potassium.
Herbal teas, in particular yarrow, lemon balm, black haw, chamomile, red raspberry, wild strawberry, valerian, and raspberry leaf all help - my foster daughter swears by raspberry leaf. Try the Chinese medicine Bupleurum (xiao yao wan) get her to take 3-4 tablets 4 times a day a few weeks her periods. Also take Evening Primrose oil or Black Cohosh capsules or Chaste Tree tincture daily to regulate hormones to help prevent cramps.
Obviously she shouldn't use tampons, as well as her age putting her at higher risk of TSS and infections from tampon use, they would also be more likely to contribute to cramps. Cups are much safer, cleaner and more convenient and reliable for all women, but particularly girls her age, and of course not only do they not cause cramps like tampons, but they actually lessen or can even stop cramps. Research has also shown women have more positive attitudes towards their periods when using cups, which also improves general menstrual health - seriously.
If all else fails get her on an anti-inflammatory drug such as Mefenamic acid to block the the synthesis of prostaglandin F2 alpha, a hormone responsible for cramps. She'd take these 3 times a day for the first 4 days of her period.
And they are just a very few ideas.