Dude, you obviously have more concern for her than her parents.
I dont know about where you live but here we just phone the dr and make an appointment. Teens dont need their parents to accompany them.
We also have a phone hotline called telehealth that is staffed 24 hrs by nurses who will assess a condition and determine if a dr is warranted or an er trip they also suggest home remedies until a dr can be seen..
Not every place is as fortunate to have these services though.
If you do, use it. If not, talk to your grandma about it. She can give you another perspective and I assume you trust her judgement. If you decide to wait till monday to see a doc, phone the appointment in yourself. Then, have her tell her parents she has an appointment and would like them to come. If they refuse go without them.
If they agree great. Either way they will have gotten a wake up call from their daughter that she isnt going to neglect her health just because they are.
If her parents wont take the responsibility on it is her responsibility to do it herself.
If you all decide to go to the er do the same thing. Offer her parents a chance to come and support her concerns. Its up to them if they go or not but they cant stop her from taking care of her own body.

I need to stress though that the er is for emergencies and if it can wait...wait. If not...get going.
I hope it all works out good.
Peace.