Welcome to the forum. Thanks for your question and for your kind comment about our services.
I agree exactly with your doctor: no need for worry, as long as you follow his or her advice about repeat pap smears and perhaps HPV tests in the future. With a normal pap smear, a positive test for HPV of any type -- including a high risk type like HPV-16 or 18 -- is not cause for alarm. This test result increases the risk of cancer or future pre-cancerous changes in your cervix, but most such infections clear up on their own and never lead to cancer. And progression to cancer typically takes several years; if and when a pap smear becomes abnormal, there will still be plenty of time for effective treatment to prevent a serious outcome.
And most HPV infections clear up on their own. Most likely future HPV tests will be negative, indicating your immune system has cleared the infection.
And don't let the Michael Douglas business bother you. His cancer is oral, not genital. And in any case, awareness of any particular case of a serious outcome of HPV doesn't change your risk of such an outcome. Your situation is similar to that of thousands and thousands of women every year -- perhaps a million of you in the US alone. Almost none of them will have any serious health problem from their genital HPV infections.
Take a look at the thread linked below for more information about genital HPV infection, then let me know if there is still anything you don't understand.
http://www.medhelp.org/posts/STDs/HPV-Transmission/show/1522088
Best wishes-- HHH, MD