headache, dizziness, and wrong words coming out

If it were me or a loved one with those symptoms, I'd get to the nearest urgent care clinic or emergency room because those could be symptoms of a stroke.

At the very least, make a call to your doctor's office and leave a message with the answering service to have the doctor on call give you advice as to whether you should go to an emergency room.

Ok. First a stroke is not likely, it will not be in the basic differential diagnosis for these particular set of symptoms. And is kind of scary to say something like that to a 20 yo girl.
I will consider first Migraine (classic subtype), vascular headache, Horton´s headache, trigemial neuralgia, stress headache. All of them are not mortal diseases but are really dificult to diferentiate without an appropiate clinical evaluation.
You must go to a Doctor of your trust.
My particular guess without having more information and using my experience will be migraine. They are painfull stubborn diseases that are sometimes difficult to control and need long term treatments.
I´ve seen many patients that auto prescribe them selves mulitple over the counter drugs, and te only thing they do is delay an appropiate diagnosis and suffer for weeks or moths without need.
The are other nasty diseases that can cause similar symptoms but are rare and usually give more symptoms, and considering the your background i wouldnt bother yet for such yet.
So stay calm and make an appointment.

For all we know she could be hungover.

You are completelly correct, i am at work right now and you really made me laugh out loud. You are surely correct. It can be a hangover. Women are more sensitive to alcohol side effects. I´ve seen lately many young people having drinking marathons. So yes thats something to rule out too.

This is excellent advice kids: Never go to a doctor you don't trust.