Student Going Home with COVID SX Without Seeing Nurse

I had a teacher send me an email saying that a student was not feeling well (sore throat, runny nose) and she wanted to send her to me. Student is 18 y.o. and didn’t want to come to me so she signed herself out. I followed up with her after school and she confirmed her sx but is not wanting to get COVID tested.

Am I able to put her out for 10 days or is she able to come back when she reports she is feeling well? She is scheduled for the vaccine tomorrow so I don’t want her to say she’s feeling well (and actually not be well) and come tomorrow just for the vaccine .