Yes, the virus will remain. Every virus you get never really goes away. HPV works the same. Once the tests come back negative, the HPV is still there and you probably will never have a recurrence, or be able to transmit it to a future partner. Some HPV infections do persist for life, but 98% do not. 92% of people have no signs or symptoms of HPV within 6-12 months after infection, and they never have a recurrence.
80% of sexually active adults will get HPV in their lifetime. It sucks, I had it, but it’s nothing to freak out about. You will be okay 
Just check in with the doctor.