I agree with your doctor and disagree with "wont fully go away because its a virus and they stay with you for forever." It might be true in the sense that there will be some remnets of infection, but this isn't how most viruses are viewed.
For example, when you catch a cold (Rhinovirus) of influenza, we don't say that you will have the virus forever. Your immune system will respond, clear the virus, and the next time you get a cold, it will be from a new infection caused by a different strain, not from reactivcation of a previous infection.
Simmilarily, studies show that within 24 months, but this often is acheived in less time, 90% women who test positive for HPV, will have negative test results. It is uncommon to test postitve for the same strain of HPV again.
But uncommon doesn't mean never, and in a small minority of people, the virus persists or causes problems in the future. This is why continued Paps are so important.
So while viral DNA might not be completely eliminated, and reoccurances can happen, i don't think HPV needs to be viewed as a permanent infection.
no just use protection, it might "clear up on it own" but wont fully go away because its a virus and they stay with you for forever. you can still have sex and it going to change the results. your next pap smear might be "normal" the HPV could show up on your next pap or it might not.