Sometimes, rigid rules need to be broken. I would lighten up on that if I were you. I am not saying they stay home 1-2 days every month but there are times it is best if someone stays home... rule or no rule.
My almost 20yr old had horrendous cramping and was very sick about once every 6 months. Every other time was the normal, just bad cramping.
Of course, I allowed her to stay home during the bad times and I know a lot of moms who do the same. When they are in that much pain and sick on top of that, they should not be at school.
By age 16, our daughter's bad months were more frequently and she basically never stopped bleeding. She has a close relationship with her pedi who will see her until she is out of college. She went on a low dose hormone to regulate her cycle. It took about 3 rounds of meds to get the "right" fit and she has been on the hormone (bcp) ever since. She still occasionally gets bad cramping that will keep her in bed a day but nothing like the times before with throwing up, diarrhea. At least she is able to manage it now.
She did not have any invasive exam and her pedi did not recommend one at the time either. It is not conclusive that an internal exam will be done. They can use ultrasound and other measures at her age. She did have extensive blood work to rule out any issues and to check all of her levels. She continues to have routine blood work since being on the hormone as a proactive measure by her pedi.
I never would have considered making her go to school on those worst days. She is a good student (4.0) and hates to miss school and fights missing any school because makeup work is a lot harder than being in class. I would not put that undue pressure on my daughter.
I did allow her access to her medications but I also knew how much she was taking and made sure she was aware of dosage limits per each 24 hours. Be careful about not knowing how much she is taking so she does not accidently do any damage to herself with possible overdose.
Call the pedi and ask what you can do to help get relief for your daughter. She already feels pressure to go to school tomorrow no matter how she feels. That is not fair in my mind.. She is sick and she needs to be healthier to get back in school so her immune system can be stronger and hopefully not catch any other bugs going around at school. It is not always black and white with rules... sometimes we need so ease up on strict rules. It does not make you less of a parent, it makes you more of a caring concerned parent.
She may need a stronger pain relief med at times and that is ok. I know it is hard for her, and you. Hang in there and get some help from the pedi.