I`m a student too. I think that you can use:
I try to persuade her but she has not wanted to visit the doctor.
because persuade is a transitive verb so always you need to use "to"
Also you can use other ways to give an advice:
I would suggest going to the doctor
How about going to the doctor?
Have you tried going to the doctor?
The expressions i would suggest, how about and have you tried are followed by gerunds.
Why donīt you go to the doctor?
You could go to the doctor
If I were you, I would go to the doctor